Law of conservation of mass and energy. Basic laws of chemistry Laws of conservation in chemistry
Among the fundamental laws of chemistry is the law of conservation of mass of substances, which was formulated as a general concept conservation of matter and motion by the great Russian scientist M.V. Lomonosov in 1748 and confirmed experimentally by himself in 1756 and independently by the French chemist A.-L. Lavoisier in 1773.
Modern wording of the law:
the mass of substances that entered into a chemical reaction is equal to the mass of substances formed as a result of the reaction.
That is, in chemical reactions the number of atoms before and after the reaction remains the same, for example: H 2 SO 4 + 2NaOH = Na 2 SO 4 + 2 H 2 O.
However, almost all reactions are accompanied by the release or absorption of heat. The interaction of acid and alkali always involves the release of energy into the environment (exothermic reaction), so the above equation does not fully reflect the process. It would be more correct to write this reaction as follows
H 2 SO 4 + 2NaOH = Na 2 SO 4 + 2 H 2 O + Q, where Q is 113.7 kJ.
Is there a contradiction here with the law of conservation of mass of substances?
Much later, in 1905, A. Einstein established a quantitative relationship between the mass m and the energy of the system E: E = m ∙ c 2, where c is the speed of light in vacuum (about 300,000 km/s or 3∙10 10 cm/s ). Using Einstein's equation, we determine the change in mass (in grams) for our reaction
Δm = Δ E/s 2 = (113.7 ∙10 10 g∙cm 2 /g)/ (3∙10 10 cm/s) 2 = 1.26 ∙10 –9 g.
It is currently impossible to detect such negligible changes in mass. Therefore, the law of conservation of mass of substances is practically valid for chemical reactions, but theoretically it is not strict - it cannot be applied to processes that are accompanied by the release of a very large amount of energy, for example, to thermonuclear reactions.
So, the law of conservation of mass and the law of conservation of energy do not exist separately from each other. One law manifests itself in nature - the law of conservation of mass and energy. Like other laws of nature, the law of conservation of mass of substances has great practical significance. Thus, using it, it is possible to establish quantitative relationships between substances undergoing chemical transformations.
In a chemical reaction equation, each formula represents one mole of the corresponding substance. Therefore, knowing the molar masses of the substances participating in the reaction, we can use the reaction equation to find the relationship between the masses of the substances that react and those formed as a result. If the reaction involves substances in the gaseous state, then the reaction equation allows one to find their volume ratios.
So, calculations using chemical equations, i.e. stoichiometric calculations, are based on the law of conservation of mass of substances. However, in real conditions, due to incomplete processes or various losses, the mass of the resulting products is often less than the mass that should be according to the law of conservation of mass of substances.
Yield of reaction product(or mass fraction of yield) is the ratio, expressed as a percentage, of the mass of the actually obtained product to its mass, which should be obtained in accordance with the theoretical calculation:
η = m (X) / m theor. (X),
where η is the product yield, %; m (X) – mass of product X obtained in the real process; m theor. (X) – theoretically calculated mass of substance X.
In those tasks where the product yield is not specified, it is assumed that it is quantitative, i.e. η = 100%.
EXAMPLES OF SOLVING PROBLEMS (calculations using chemical equations)
Task 1. Iron can be obtained by reducing iron(III) oxide with aluminum. Determine how much aluminum is required to obtain 140 g of iron?
Solution 1. Let's write the reaction equation: Fe 2 O 3 + 2Al = 2 Fe + Al 2 O 3
Let's determine the amount of iron substance that needs to be obtained:
ν (Fe) = m (Fe)/ M(Fe) = 140 g/ 56 g/mol = 2.5 mol.
From the reaction equation it is clear that to obtain iron in an amount of 2 moles of a substance, 2 moles of aluminum are required, i.e.
ν (Al)/ ν (Fe) = 2/2, therefore ν (Al) = ν (Fe) = 2.5 mol.
Now you can determine the mass of aluminum:
m (Al) = M(Al)∙ ν(Al) = 27 g/mol ∙ 2.5 mol = 67.5 g.
Answer: to obtain 140 g of iron you will need 67.5 g of aluminum.
Solution 2. Such problems can be solved by drawing up proportions. From the reaction equation it is clear that to produce iron in an amount of 2 moles of a substance, 2 moles of aluminum are required. Let's write down:
To obtain (2∙56) g = 112 g Fe, (2∙27) g = 54 g Al is required
» » » » 140 g Fe » » » » m (Al)
Let's make a proportion: 112: 54 = 140: m(Al), from here it follows
m(Al) = 140 ∙ 54 /112 = 67.5 g
Task 2. What volume of hydrogen will be released (normal conditions) if 10.8 g of aluminum are dissolved in excess hydrochloric acid?
Solution. Let's write the reaction equation: 6HCl + 2Al = 2AlCl 3 + 3H 2
Let us determine the amount of aluminum substance that reacted
ν (Al) = m (Al)/ M (Al) = 10.8 g / 27 g/mol = 0.4 mol.
From the reaction equation it follows that when 2 moles of aluminum are dissolved, 3 moles of hydrogen H2 are obtained, i.e. ν (Al)/ ν (H 2) = 2/3, therefore,
ν (H 2) = 3 ν (Al)/2 = 3 ∙0.4 mol/2 = 0.6 mol.
Let's calculate the volume of hydrogen:
V(H 2) = V M ∙ ν (H 2) = 22.4 l/mol ∙ 0.6 mol = 13.44 l.
Answer: when 10.8 g of Al is dissolved in hydrochloric acid, 13.44 liters of hydrogen will be obtained.
Task 3. What volume of sulfur (IV) oxide must be oxidized with oxygen to obtain 20 g of sulfur (VI) oxide? Conditions are normal, product yield is 80%.
Solution. Let's write the reaction equation: 2SO 2 + O 2 = 2SO 3
Let us determine the mass of sulfur oxide (VI), which is obtained in the quantitative yield of the product (i.e. theoretically), using the formula
η = m (X) / m theor. (X),
where η is equal to 0.8 (or 80%) according to the conditions of the problem.
It follows: m theor (SO 3) = m (SO 3) / η(SO 3) = 20/0.8 = 25 g.
How much sulfur (VI) oxide substance is 25 g is determined by the formula
ν (SO 3) = m (SO 3)/ M (SO 3) = 25 g/(32 +3∙16) g/mol = 25/80 = 0.3125 mol.
From the reaction equation it follows that
ν (SO 2)/ ν (SO 3) = 2/2, therefore
ν (SO 2) = ν (SO 3) = 0.3125 mol.
It remains to determine the volume of sulfur oxide (IV) under normal conditions: V o (SO 2) = V M ∙ ν (SO 2) = 22.4 l/mol ∙ 0.3125 mol = 7 l.
Answer: to obtain 20 g of sulfur oxide (VI) you will need 7 liters of sulfur oxide (IV).
Problem 4. To a solution containing 25.5 g of silver nitrate was added a solution containing 7.8 g of sodium sulfide. What is the mass of the sediment formed?
Solution. Let us write the equation of the ongoing reaction:
2AgNO 3 + Na 2 S = Ag 2 S↓ + 2NaNO 3.
Since the amount of the substance and the mass of the product are calculated based on the mass and amount of the substance taken in deficiency, therefore, it is first necessary to determine the amounts of the substances silver nitrate and sodium sulfide:
ν (AgNO 3) = m (AgNO 3) / M (AgNO 3) = 25.5 g / 170 g/mol = 0.15 mol;
ν (Na 2 S) = m (Na 2 S)/ M (Na 2 S) = 7.8 g / 78 g/mol = 0.1 mol.
According to the reaction equation: for every 2 moles of AgNO 3, 1 mole of Na 2 S is required (i.e., half as much), which means:
per 0.15 mol AgNO 3 » » » » ν ’ mol Na 2 S.
Then ν ’ (Na 2 S) = ½ ∙ 0.15 mol = 0.075 mol,
therefore, sodium sulfide is taken in excess and the calculation must be carried out based on the amount of AgNO 3 substance.
From the reaction equation it follows:
ν(Ag 2 S) = ν (Na 2 S) = ν (AgNO 3)/2 = 0.15 mol/2 = 0.075 mol.
Now we can determine the mass of silver sulfide that precipitated: m(Ag 2 S) = M(Ag 2 S) ∙ ν(Ag 2 S) = 248 g/mol ∙ 0.075 mol = 18.6 g.
Answer: The mass of the formed sediment is 18.6 g.
Law of Multiples
What happens if two elements can form multiple chemical compounds with each other? In 1803, the great English chemist J. Dalton showed:
● If two elements form several compounds with each other, then the masses of one of the elements that fall on the same mass of the other are related to each other as small integers.
This law confirmed the atomistic ideas about the structure of matter: since elements are combined in multiple ratios, therefore, chemical compounds differ by an integer number of atoms. They represent the smallest amount of element entering a compound. For example, per 1 g of nitrogen in its oxides N 2 O, NO, N 2 O 3, NO 2, N 2 O 5 there is 0.57; 1.14; 1.71; 2.28; and 2.85 g of oxygen, which corresponds to a ratio of 1:2:3:4:5.
However, in the case of compounds of variable composition, the law of multiple ratios is not applicable.
Law of Constancy of Composition
This law was discovered by the French scientist J. Proust in 1801:
● Any chemically pure individual substance always has the same quantitative composition, regardless of the method of its preparation.
For example, sulfur dioxide can be produced by burning sulfur or by the action of acids on sulfites, or by the action of concentrated sulfuric acid on copper. In any case, a sulfur dioxide molecule will consist of one sulfur atom and two oxygen atoms - SO 2, i.e. the mass ratio of sulfur and oxygen is always 1:1.
Proust's law was of fundamental importance for chemistry - it led to the idea of the existence of molecules and confirmed the indivisibility of atoms. Substances of constant composition were called “daltonides” in honor of Dalton.
The law of constancy of composition is also valid only for substances of molecular structure. Currently, a large number of compounds are known that do not obey the law of constancy of composition and the law of multiple ratios; they are called compounds of variable composition (most often these are oxides, sulfides, nitrides, hydrides, etc.) . In such compounds, per unit mass of one element there may be a different mass of another element. For example, the composition of titanium (II) and (IV) oxides, depending on the synthesis conditions, can be as follows: TiO 0.8–1.2 and TiO 1.9–2.0.
Compounds of variable composition are obtained due to defects in the crystal lattice during the crystallization of the substance. Due to the presence of voids or excess atoms in the crystal lattice, some materials exhibit many new and interesting properties, such as semiconductor properties.
Law of equivalents
Studying the ratio of the masses of acids and bases interacting with each other to form salts, I. Richter in 1792 - 1800. came to the conclusion that the masses of one substance reacting with the same mass of another substance are related to each other as simple integers. Later, D. Dalton introduced the concept of “connecting weight”, which has now been replaced by the concept of equivalent.
● Substances react with each other in quantities proportional to their equivalents.
To solve some problems, another formulation of this law is used:
● The masses (volumes) of substances reacting with each other are proportional to their equivalent masses (volumes):
m A /m B = E A /E B,
where m A and m B are the masses of reactants A and B,
E A and E B are the equivalent masses of these substances.
GAS LAWS
Systems. Unlike the classical model, the mass of only an isolated physical system is conserved, that is, in the absence of energy exchange with the external environment. The sum of the masses of the system components is not preserved (the mass is non-additive). For example, during radioactive decay in an isolated system consisting of matter and radiation, the total mass of the matter decreases, but the mass of the system remains the same, despite the fact that the mass of radiation may be zero.
Historical sketch
The law of conservation of mass has historically been understood as one of the formulations law of conservation of matter. One of the first to formulate it was the ancient Greek philosopher Empedocles (5th century BC):
Nothing can come from nothing, and there is no way that what exists can be destroyed.
Earlier, Empedocles’ “principle of conservation” was used by representatives of the Milesian school to formulate theoretical ideas about the primal substance, the basis of all things. Later, a similar thesis was expressed by Democritus, Aristotle and Epicurus (as retold by Lucretius Cara).
Medieval scientists also did not express any doubts about the truth of this law. Francis Bacon declared in 1620: “The sum of matter remains always constant, and cannot be increased or diminished... not one small part of it can be either overcome by the whole mass of the world, or destroyed by the combined force of all agents, or in any way destroyed.”
Weight is so closely tied to the substance of the elements that, changing from one to another, they always retain the same weight.
Original text (French)
La pesanteur est si étroitement jointe à la première matière des éléments que, se changeant de l"un en l"autre, ils gardent toujours le même poids.
All changes occurring in nature occur in such a way that if something is added to something, it is taken away from something else. Thus, as much matter is added to one body, the same amount is lost from another, how many hours I spend sleeping, the same amount I take away from being awake, etc.
In the USSR, on the basis of this phrase, M.V. Lomonosov was declared the author of the law of conservation of mass, although he never claimed such a priority and does not mention this law in his “Review of the Most Important Discoveries.” Modern historians consider such claims to be unfounded. It is a mistaken opinion that the law of conservation of mass was proven experimentally by Lomonosov;
The universal law was formulated by Lomonosov on the basis of general philosophical materialistic considerations; he was never questioned or tested by him, but on the contrary, served him as a firm starting position in all his studies throughout his life.
Subsequently, until the creation of microworld physics, the law of conservation of mass was considered true and obvious. Immanuel Kant declared this law a postulate of natural science (1786). Lavoisier in his “Elementary Textbook of Chemistry” (1789) gave a precise quantitative formulation of the law of conservation of mass of matter, but did not declare it some new and important law, but simply mentioned it in passing as a long-known and reliably established fact. For chemical reactions, Lavoisier formulated the law in the following expressions:
Nothing happens either in artificial processes or in natural ones, and one can put forward the position that in every operation [chemical reaction] there is the same amount of matter before and after, that the quality and quantity of the principles remained the same, only displacements and regroupings occurred. The entire art of doing experiments in chemistry is based on this proposition.
In other words, the mass of a closed physical system in which a chemical reaction occurs is conserved, and the sum of the masses of all substances that entered into this reaction is equal to the sum of the masses of all reaction products (that is, it is also conserved). The mass is thus considered additive.
Current state
In the 20th century, two new properties of mass were discovered.
(M1) The mass of a physical object depends on its internal energy (see Equivalence of mass and energy). When external energy is absorbed, the mass increases, and when it is lost, it decreases. It follows that mass is conserved only in an isolated system, that is, in the absence of energy exchange with the external environment. The change in mass during nuclear reactions is especially noticeable. But even during chemical reactions that are accompanied by the release (or absorption) of heat, the mass is not conserved, although in this case the mass defect is negligible. Academician L. B. Okun writes:
To emphasize that the mass of a body changes whenever its internal energy changes, consider two common examples:
1) when an iron iron is heated by 200°, its mass increases by Δ m / m ≈ 10 − 12 (\displaystyle \Delta m/m\approx 10^(-12)); 2) when a certain amount of ice is completely converted into water Δ m / m ≈ 3.7 ⋅ 10 − 12 (\displaystyle \Delta m/m\approx 3.7\cdot 10^(-12)).
(M2) Mass is not an additive quantity: the mass of a system is not equal to the sum of the masses of its components. Examples of non-additivity:
- An electron and a positron, each of which has mass, can annihilate into photons, which do not have mass individually, but have it only as a system.
- The mass of a deuteron, consisting of one proton and one neutron, is not equal to the sum of the masses of its components, since the interaction energy of the particles must be taken into account.
- In thermonuclear reactions occurring inside the Sun, the mass of hydrogen is not equal to the mass of the helium produced from it.
- A particularly striking example: the mass of a proton (≈938 MeV) is several tens of times greater than the mass of its constituent quarks (about 11 MeV).
Thus, during physical processes that are accompanied by the disintegration or synthesis of physical structures, the sum of the masses of the constituents (components) of the system is not conserved, but the total mass of this (isolated) system is preserved:
- The mass of the system of photons resulting from annihilation is equal to the mass of the system consisting of the annihilating electron and positron.
- The mass of a system consisting of a deuteron (taking into account the binding energy) is equal to the mass of a system consisting of one proton and one neutron separately.
- The mass of a system consisting of helium resulting from thermonuclear reactions, taking into account the released energy, is equal to the mass of hydrogen.
This means that in modern physics the law of conservation of mass is closely related to the law of conservation of energy and is fulfilled with the same limitation - the exchange of energy between the system and the external environment must be taken into account.
Pre-relativistic physics knew two fundamental conservation laws, namely: the law of conservation of energy and the law of conservation of mass; both of these fundamental laws were considered completely independent of each other. The theory of relativity merged them into one.
In more detail
To explain in more detail why mass in modern physics turns out to be non-additive (the mass of the system is not equal - generally speaking - to the sum of the masses of the components), it should first be noted that under the term weight in modern physics the Lorentz-invariant quantity is understood:
m = E 2 / c 4 − p 2 / c 2 , (\displaystyle m=(\sqrt (E^(2)/c^(4)-p^(2)/c^(2))),)Where E (\displaystyle E)- energy, p → (\displaystyle (\vec (p)))- impulse, c (\displaystyle c)- speed of light. And we immediately note that this expression is equally easily applicable to a point structureless (“elementary”) particle, and to any physical system, and in the latter case, the energy and momentum of the system are calculated simply by summing the energies and momenta of the components of the system (energy and momentum are additive) .
- You can also note in passing that the momentum-energy vector of the system is a 4-vector, that is, its components are transformed upon transition to another reference system in accordance with Lorentz transformations, since its terms are transformed in this way - 4-vectors of the energy-momentum of the particles that make up the system. And since the mass defined above is the length of this vector in the Lorentz metric, it turns out to be invariant (Lorentz-invariant), that is, does not depend on the reference system in which it is measured or calculated.
In addition, we note that c (\displaystyle c)- a universal constant, that is, just a number that never changes, therefore, in principle, you can choose such a system of units of measurement so that c = 1 (\displaystyle c=1), and then the mentioned formula will be less cluttered:
m = E 2 − p 2 , (\displaystyle m=(\sqrt (E^(2)-p^(2))),)as well as other formulas associated with it (and below, for brevity, we will use just such a system of units).
Having already considered the most seemingly paradoxical case of violation of mass additivity - the case when a system of several (for simplicity, we will limit ourselves to two) massless particles (for example, photons) can have a non-zero mass, it is easy to see the mechanism that gives rise to non-additivity of mass.
Let there be two photons 1 and 2 with opposite momenta: p → 1 = − p → 2 (\displaystyle (\vec (p))_(1)=-(\vec (p))_(2)). The mass of each photon is zero, therefore we can write:
0 = E 1 2 − p 1 2 , (\displaystyle 0=(\sqrt (E_(1)^(2)-p_(1)^(2))),) 0 = E 2 2 − p 2 2 , (\displaystyle 0=(\sqrt (E_(2)^(2)-p_(2)^(2))),)that is, the energy of each photon is equal to the modulus of its momentum. Let us note in passing that the mass is equal to zero due to the subtraction of non-zero quantities from each other under the root sign.
Let us now consider the system of these two photons as a whole, calculating its momentum and energy. As we see, the momentum of this system is zero (the photon pulses, having added up, were destroyed, since these photons fly in opposite directions):
p → = p → 1 + p → 2 = 0 → . (\displaystyle (\vec (p))=(\vec (p))_(1)+(\vec (p))_(2)=(\vec (0)).).The energy of our physical system will be simply the sum of the energies of the first and second photons:
E = E 1 + E 2. (\displaystyle E=E_(1)+E_(2).)Well, hence the mass of the system:
m = E 2 − p 2 = E 2 − 0 = E ≠ 0 , (\displaystyle m=(\sqrt (E^(2)-p^(2)))=(\sqrt (E^(2)- 0))=E\neq 0,)(the impulses were destroyed, but the energies were added - they cannot be of different signs).
In the general case, everything happens similarly to this, the most clear and simple example. Generally speaking, the particles forming a system do not necessarily have to have zero masses, it is enough for the masses to be small or at least comparable to the energies or momenta, and the effect will be large or noticeable. It is also clear that there is almost never an exact additivity of mass, with the exception of very special cases.
Mass and inertia
The lack of additivity of mass would seem to introduce difficulties. However, they are redeemed not only by the fact that the mass defined this way (and not otherwise, for example, as energy divided by the square of the speed of light) turns out to be Lorentz-invariant, a convenient and formally beautiful quantity, but also has a physical meaning that exactly corresponds to the usual classical understanding of mass as a measure of inertia.
Namely, for the reference system of rest of a physical system (that is, the reference system in which the momentum of the physical system is zero) or reference systems in which the rest system moves slowly (compared to the speed of light), the above-mentioned definition of mass
m = E 2 / c 4 − p 2 / c 2 (\displaystyle m=(\sqrt (E^(2)/c^(4)-p^(2)/c^(2))))Fully corresponds to the classical Newtonian mass (included in Newton's second law).
This can be specifically illustrated by considering a system that on the outside (for external interactions) is an ordinary solid body, but on the inside containing fast moving particles. For example, by considering a mirror box with perfectly reflective walls, inside of which there are photons (electromagnetic waves).
For simplicity and greater clarity of the effect, let the box itself be (almost) weightless. Then, if, as in the example discussed in the paragraph above, the total momentum of the photons inside the box is zero, then the box will be generally motionless. Moreover, under the influence of external forces (for example, if we push it), it must behave like a body with a mass equal to the total energy of the photons inside, divided by c 2 (\displaystyle c^(2)).
Let's look at this qualitatively. Let us push the box, and because of this it has acquired some speed to the right. For simplicity, we will now talk only about electromagnetic waves traveling strictly to the right and left. An electromagnetic wave reflected from the left wall will increase its frequency (due to the Doppler effect) and energy. A wave reflected from the right wall, on the contrary, will reduce its frequency and energy during reflection, but the total energy will increase, since there will not be complete compensation. As a result, the body will acquire kinetic energy equal to m v 2 / 2 (\displaystyle mv^(2)/2)(If v<<
c
{\displaystyle v<
The mass of substances entering into a chemical reaction is equal to the mass of substances formed as a result of the reaction.
The law of conservation of mass is a special case of the general law of nature - the law of conservation of matter and energy. Based on this law, chemical reactions can be represented using chemical equations, using chemical formulas of substances and stoichiometric coefficients that reflect the relative quantities (number of moles) of substances involved in the reaction.
For example, the combustion reaction of methane is written as follows:
Law of conservation of mass of substances
(M.V. Lomonosov, 1748; A. Lavoisier, 1789)
The mass of all substances involved in a chemical reaction is equal to the mass of all reaction products.
The atomic-molecular theory explains this law as follows: as a result of chemical reactions, atoms do not disappear or appear, but their rearrangement occurs (i.e., a chemical transformation is the process of breaking some bonds between atoms and forming others, as a result of which from the original molecules substances, molecules of reaction products are obtained). Since the number of atoms before and after the reaction remains unchanged, their total mass should also not change. Mass was understood as a quantity characterizing the amount of matter.
At the beginning of the 20th century, the formulation of the law of conservation of mass was revised in connection with the advent of the theory of relativity (A. Einstein, 1905), according to which the mass of a body depends on its speed and, therefore, characterizes not only the amount of matter, but also its movement. The energy E received by a body is related to the increase in its mass m by the relation E = m c 2, where c is the speed of light. This ratio is not used in chemical reactions, because 1 kJ of energy corresponds to a change in mass by ~10 -11 g and m practically cannot be measured. In nuclear reactions, where E is ~10 6 times greater than in chemical reactions, m should be taken into account.
Based on the law of conservation of mass, it is possible to draw up equations of chemical reactions and make calculations using them. It is the basis of quantitative chemical analysis.
Law of Constancy of Composition
Material from Wikipedia - the free encyclopedia
Law of constancy of composition ( J.L. Proust, 1801 -1808.) - any specific chemically pure compound, regardless of the method of its preparation, consists of the same chemical elements, and the ratios of their masses are constant, and relative numbers their atoms are expressed as integers. This is one of the basic laws chemistry.
The law of constancy of composition is not satisfied for Berthollides(compounds of variable composition). However, for the sake of simplicity, the composition of many Berthollides is written as constant. For example, composition iron(II) oxide written as FeO (instead of the more precise formula Fe 1-x O).
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LAW OF CONSTANT COMPOSITION |
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According to the law of constancy of composition, every pure substance has a constant composition, regardless of the method of its preparation. So, calcium oxide can be obtained in the following ways:
Regardless of how the substance CaO is obtained, it has a constant composition: one calcium atom and one oxygen atom form the calcium oxide molecule CaO. Determine the molar mass of CaO:
We determine the mass fraction of Ca using the formula:
Conclusion: In a chemically pure oxide, the mass fraction of calcium is always 71.4% and oxygen 28.6%. |
Law of Multiples
The law of multiple ratios is one of stoichiometric laws chemistry: if two substances (simple or complex) form more than one compound with each other, then the masses of one substance per one and the same mass of another substance are related as whole numbers, usually small.
Law of conservation of mass and energy
In nuclear reactions, the changes in energy are so significant that the equivalence of mass and energy can no longer be neglected. If you monitor the change in mass alone, it seems that the conservation law is violated.
To see this, consider the relationship between mass and energy in units of the atomic mass scale. Then into the equation e = mc 2 will include more than 1 G mass, and mass 1 on the atomic weight scale, approximately equal to the weight of the nucleus of a hydrogen atom-1, the lightest known atomic nucleus. In reality, the mass of 1 on the atomic scale is 1.67 · 10 -24 G.
Despite the enormous magnitude of c 2, the energy equivalent to such an insignificant mass is only 0.0015 erg.
On normal everyday scales 0.0015 erg Indeed, the value is small, but on the atomic scale it is equal to approximately one billion electron volts - this is already an impressive figure. According to recent measurements, the mass of 1 on the atomic scale is equivalent to 0.931478 Gav or 931.478 Mev.
If we put the mass of the hydrogen nucleus equal to 1.00797, it will be equivalent to an energy of 0.938 905 Bev, and the mass of four such hydrogen nuclei is equivalent to an energy of 3.75562 Gav. On the other hand, the mass of a helium nucleus, equal to 4.00280 on the atomic weight scale, is equivalent to an energy of 3.72803 Gav. When four hydrogen nuclei are converted into one helium nucleus, the mass loss is therefore 0.02759 Gav or 27.59 Mev. The measured amount of energy released during this reaction turned out to be very close to the theoretical one. Research has shown that in all nuclear reactions of this type, the energy released corresponds to the mass lost according to Einstein's equation. As a result, it has become customary to speak not about the law of conservation of only mass or only energy, but about the law of conservation of mass and energy. However, we can simply talk about the law of conservation of energy, meaning that mass is a form of energy. This is exactly what I will do in the future.
Let us now return to the source of solar energy. If indeed it arises from the transformation of hydrogen nuclei into helium, the colossal energy that is generated and radiated into the surrounding space must be balanced by the equivalent disappearance of mass.
The total radiation energy of the Sun, as I already said, is 5.6 · 10 27 cal/min, which is equivalent to 3.8 · 10 33 erg/sec. Dividing by c 2, we find that the radiation of this
energy equivalent to a loss of 4.2 · 10 12 G in 1 sec, or 276,000,000 T in 1 min.
According to the meteorite theory of solar radiation, every minute 1.2 · 10 20 G meteorite matter. This constant addition to the solar mass reduces the length of each year by two seconds. The loss of mass during the conversion of hydrogen to helium is approximately one thirty-millionth of the increase in mass required by the meteorite theory. As a result of the loss of solar mass due to nuclear reactions, the year would increase by only one second in fifteen million years. The change in the length of the year is difficult to detect and has no practical significance for us.
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From book 1. Modern science of nature, laws of mechanics author Feynman Richard PhillipsLaw of conservation of mechanical energy We have seen from the examples just discussed how useful it is to know a quantity that does not change its numerical value (conserved) during movement. So far we know such a quantity only for one body. And if it moves in the field of gravity
From the author's bookLaw of Conservation of Rotational Momentum If you tie two stones with a rope and forcefully throw one of them, the second stone will fly after the first on a taut rope. One stone will overtake the second, moving forward will be accompanied by rotation. Let's forget about the field
From the author's bookTHIRD PROBLEM: HOW TO INCREASE THE ACCELERATION POWER OF HUMAN MASS - USING SOLAR ENERGY Of the three possible solutions to the main problem of increasing human energy, this is the most important to sort out. Not only because of its own meaning, but also because of the underlying
From the author's book 2.1. Finding the common cause of ppm failures. “The Law of Conservation of Force” The last two centuries described in Chap. 1 period of ppm history (XVII and XVIII centuries) are characterized by the fact that many, even quite serious scientists, believed that a perpetual motion machine could be created. Even constant failures From the author's book From the author's bookIII. The law of the relationship between mass and energy 1. Einstein's formula. We know that there is a law of conservation of mass: “Nothing in nature disappears without a trace and is not created from nothing, everything transforms.” On the other hand, it is known that there is a law of conservation of energy. Energy
From the author's bookChapter 10 LAW OF CONSERVATION OF MOMENTUM § 1. Newton’s Third Law§ 2. Law of Conservation of Momentum§3. The momentum is still conserved§ 4. Momentum and energy§ 5. Relativistic momentum§ 1. Newton’s third lawNewton’s second law, which relates the acceleration of any body to the force acting on
The law of conservation of mass is the basis for calculating physical processes in all spheres of human activity. Its validity is not disputed by either physicists, chemists, or representatives of other sciences. This law, like a strict accountant, ensures that the exact mass of a substance is maintained before and after its interaction with other substances. The honor of discovering this law belongs to the Russian scientist M.V. Lomonosov.
Initial ideas about the composition of substances
The structure of matter remained a mystery to any person for many centuries. Various hypotheses excited the minds of scientists and prompted the sages to engage in lengthy and meaningless debates. One argued that everything consists of fire, the other defended a completely different point of view. The theory of the ancient Greek sage Democritus that all substances consist of tiny, invisible to the eye, tiny particles of matter flashed through the mass of theories and was undeservedly forgotten. Democritus called them “atoms,” which means “indivisible.” Unfortunately, for as long as 23 centuries, his assumption was forgotten.
Alchemy
Basically, the scientific data of the Middle Ages were based on prejudices and various conjectures. Alchemy arose and spread widely, which was a body of modest practical knowledge, closely flavored with the most fantastic theories. For example, famous minds of that time tried to turn lead into gold and find an unknown philosopher's stone that healed all diseases. During the search process, scientific experience gradually accumulated, consisting of many unexplained reactions of chemical elements. For example, it was found that many substances, later called simple, do not decay. Thus, the ancient theory of indivisible particles of matter was revived. It took a great mind to turn this storehouse of information into a coherent and logical theory.
Lomonosov theory
Chemistry owes its precise quantitative research method to the Russian scientist M.V. Lomonosov. For his brilliant abilities and hard work, he received the title of professor of chemistry and became a member of the Russian Academy of Sciences. Under him, the country's first modern chemical laboratory was organized, in which the famous law of conservation of mass of substances was discovered.
In the process of studying the flow of chemical reactions, Lomonosov weighed the starting chemicals and the products that appeared after the reaction. At the same time, he discovered and formulated the law of conservation of mass of matter. In the 17th century, the concept of mass was often confused with the term "weight". Therefore, masses of substances were often called “scales.” Lomonosov determined that the structure of a substance is directly dependent on the particles from which it is built. If it contains particles of the same type, then the scientist called such a substance simple. When the composition of corpuscles is heterogeneous, a complex substance is obtained. These theoretical data allowed Lomonosov to formulate the law of conservation of mass.
Definition of law
After numerous experiments, M.V. Lomonosov established a law, the essence of which was as follows: the weight of the substances that entered into the reaction is equal to the weight of the substances that resulted from the reaction.
In Russian science, this postulate is called “Lomonosov’s Law of Conservation of Mass of Substances.”
This law was formulated in 1748, and the most accurate experiments with the reaction of firing metals in sealed vessels were carried out in 1756.
Lavoisier's experiments
European science discovered the law of conservation of mass after the publication of a description of the work of the great French chemist Antoine Lavoisier.
This scientist boldly applied the theoretical concepts and physical methods of that time in his experiments, which allowed him to develop a chemical nomenclature and create a register of all chemical substances known at that time.
With his experiments, Lavoisier proved that in the process of any chemical reaction the law of conservation of mass of substances entering into a compound is observed. In addition, he expanded the extension of the law of conservation to the mass of each of the elements that took part in the reaction as part of complex substances.
Thus, the question of who discovered the law of conservation of mass of substances can be answered in two ways. M.V. Lomonosov was the first to conduct experiments that clearly demonstrated the conservation law and put it on a theoretical basis. A. Lavoisier in 1789, independently of the Russian scientist, independently discovered the law of conservation of mass and extended its principle to all elements participating in a chemical reaction.
Mass and energy
In 1905, the great A. Einstein showed the connection between the mass of a substance and its energy. It was expressed by the formula:
Einstein's equation confirms the law of conservation of mass and energy. This theory states that all energy has mass and a change in this energy causes a change in the mass of the body. The potential energy of any body is very high, and it can only be released under special conditions.
The law of conservation of mass is valid for any bodies of the micro- and macrocosm. Any chemical reaction takes part in the transformation of the internal energy of a substance. Therefore, when calculating the mass of substances participating in chemical reactions, it would be necessary to take into account the increase or loss of mass caused by the release or absorption of energy in a given reaction. In fact, in the macrocosm this effect is so insignificant that such changes can be ignored.
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