Why the concept of "amount of substance" is needed
In practice, we cannot count out the required number of molecules or atoms one by one. Substances are always taken in specific portions that can be measured using mass or volume.
In the classical calculation scheme, transitioning from the mass of the first substance to the number of its structural units, and then to the number of units and mass of the second substance, is extremely inconvenient. During calculations, one has to use excessively large or very small numbers. To bypass this problem, the concept of amount of substance was introduced.
The base unit of this quantity is the mole. One mole is a portion of a substance that contains a strictly defined number of structural units (molecules, atoms, or ions). This is a fundamental physical constant known as the Avogadro constant (number) ($N_A$). Its value is $6.02 \cdot 10^{23} \text{ mol}^{-1}$. Thus, the phrase "1 mole of water is taken" means that a portion containing $6.02 \cdot 10^{23}$ structural units of water has been selected for the reaction.
The amount of substance is calculated using the formula: $n(X) = \frac{N(X)}{N_A}$, where $N(X)$ is the number of structural units in the portion, and $N_A$ is the Avogadro constant.
Molar mass and its practical calculation
Any real portion of a chemical compound is characterized by mass ($m$) and amount of substance ($n$). The relationship between these two parameters depends on the chemical nature of the compound itself and is expressed through the molar mass ($M$).
Molar mass indicates the mass of one mole of a substance and is calculated as the ratio of mass to the amount of substance: $M(X) = \frac{m(X)}{n(X)}$. The unit of measurement is g/mol.
The Avogadro constant was chosen by chemists in such a way that the molar mass numerically coincides completely with the relative molecular mass ($M_r$), which we find by summing the atomic masses of the elements from the Periodic Table.
Let's look at an example using baking soda ($NaHCO_3$):
- The relative molecular mass is the sum of the atomic masses: $23 (Na) + 1 (H) + 12 (C) + 3 \cdot 16 (O) = 84$.
- Consequently, the molar mass $M(NaHCO_3)$ is $84$ g/mol.
Knowing this parameter, we can easily calculate the amount of substance in any sample weight. For example, $16.8$ g of soda will contain $0.20$ mol of the substance ($16.8 / 84$). Having performed this operation, we can find the number of structural units by multiplying $0.20$ mol by $6.02 \cdot 10^{23}$, which gives $1.204 \cdot 10^{23}$ molecules (or formula units).
Stoichiometry and the problem of product purity
Chemical reactions always proceed in strictly defined ratios dictated not by the actual proportions of the mixed reactants, but by the stoichiometric coefficients in the equation.
If calcium chloride ($CaCl_2$) and sodium sulfate ($Na_2SO_4$) are mixed, a precipitate of gypsum ($CaSO_4$) and a solution of table salt ($NaCl$) are formed.
- If the initial mixture was stoichiometric (the number of structural units of each reactant is precisely proportional to the coefficients — in this case 1:1), both substances will react completely without residue. The resulting $NaCl$ solution will have a purely salty taste.
- If one of the reactants was taken in excess, it will not react and will remain in the solution. Organoleptically, this will manifest as the solution becoming bitter-salty due to the impurity of the starting salt.
Solving stoichiometric problems via moles is the most rational approach. Instead of cumbersome mass proportions, we equate the amounts of substances according to the reaction equation, quickly calculate the moles of the known reactant, and use the molar mass to find the mass of the desired product.
Chemical reaction turnover
Underneath a chemical formula in a reaction equation, one always implies not an arbitrary number of particles, but a specific amount of substance (moles).
If during a practical experiment the amounts of substances precisely correspond to the stoichiometric coefficients (conventionally, there is 1 mole of substance per formula unit), it is considered that 1 turnover of the chemical reaction (or 1 mole of reaction) has been carried out. The number of completed turnovers is denoted by the Greek letter $\xi$ (xi).
For example, in the reaction $CaBr_2 + 2AgNO_3 = Ca(NO_3)_2 + 2AgBr\downarrow$, the formation of 2 mol of silver bromide precipitate corresponds to exactly 1 reaction turnover. If we experimentally obtained $56.4$ g of $AgBr$ precipitate, we can determine the number of turnovers:
- Molar mass of the product: $108 + 80 = 188$ g/mol.
- Amount of substance of the product: $56.4 / 188 = 0.3$ mol.
- Since 2 mol is 1 turnover, $0.3$ mol corresponds to $\xi = 0.3 / 2 = 0.15$.
This means that $0.15$ reaction turnovers were carried out during the synthesis.
Briefly: answers to topical questions
How to calculate the amount of a gas substance via its volume under standard conditions?
The amount of a gas substance is calculated as the ratio of its volume to the molar volume. Under standard conditions (temperature 273.15 K and pressure 101.3 kPa), the molar volume of a gas ($V_M$) has a constant value and is equal to 22.4 L/mol. The calculation formula is derived from the corollary of Avogadro's law: $n = \frac{V}{V_M}$.
How to mathematically determine which reactant is in excess?
To mathematically determine the excess, it is necessary to calculate the initial amount of substance of the reactants and compare them with the stoichiometric coefficients. In practice, the reduced amount of substance ($n'$) is calculated by dividing the initial number of moles by the corresponding coefficient in the reaction equation. The reactant that reacts completely and whose final amount is zero is the limiting reagent (in deficiency). The substance that leaves an unreacted residue after the reaction is in excess.
What is the equivalence factor and how is it calculated for acids?
The equivalence factor ($f_{eq}$) is a number indicating what fraction of a chemical entity in an acid-base reaction is equivalent to one hydrogen cation. Its value satisfies the condition $0 < f_{eq} \le 1$ and depends on the specific reaction. To determine the factor, a net ionic equation is written and it is established how many units of elementary charge the particle corresponds to.
- For the reaction $H_2SO_4 + 2KOH = K_2SO_4 + 2H_2O$: $E(H_2SO_4) = 1/2 H_2SO_4$, therefore $f_{eq} = 1/2$.
- For the reaction $H_2SO_4 + KOH = KHSO_4 + H_2O$: $E(H_2SO_4) = 1 H_2SO_4$, therefore $f_{eq} = 1$.
How to calculate the equivalent molar mass of a substance?
The equivalent molar mass of a substance is calculated by multiplying the equivalence factor by the molar mass of this substance. It represents the mass of one mole of equivalents and is measured in g/mol. The calculation formula is: $M_{eq}(B) = f_{eq} \cdot M(B)$. For example, if the equivalence factor of sulfuric acid in a reaction is $1/2$, then its equivalent molar mass will be: $1/2 \cdot 98 = 49$ g/mol.
How to calculate the molar concentration of a solution via the amount of dissolved substance?
Molar concentration is calculated as the ratio of the amount of dissolved substance to the total volume of the solution. The physical meaning of this quantity is that it shows the number of moles of a substance contained in one liter of solution. The calculation is performed using the formula: $C_m = \frac{\nu(B)}{V}$, where $\nu(B)$ (or $n$) is the amount of dissolved substance in moles, and $V$ is the volume of the solution in liters. The main unit of measurement is mol/L (for low concentrations in medicine, mmol/L is often used).
For quick calculation of the amount of substance ($n$), mass ($m$), and molar mass ($M$), imagine a triangle. Mass ($m$) is always at the top, and $n$ and $M$ are at the base. To find the required quantity, "cover" it: $n = m / M$, $m = n \cdot M$.
Class and exam questions
What is the main difference between molar mass and relative molecular mass?
They are completely numerically identical due to how the Avogadro constant is established. The only difference is that molar mass is a dimensional quantity (g/mol) showing the mass of one mole, whereas relative molecular mass is a dimensionless quantity.
How to calculate the total number of all atoms in a sample of a substance?
First, it is necessary to find the amount of substance in moles, then multiply it by the Avogadro constant to obtain the number of structural units. Finally, this value is multiplied by the sum of all atoms in a single structural unit (for example, for water $H_2O$, we multiply by 3).
What does a stoichiometric mixture mean?
This is a mixture in which the proportions of reactants ideally match the stoichiometric coefficients in the reaction equation. In this case, all starting substances will react completely, without forming a residue in the form of an excess of one of them.
What else to study on this topic
- Mechanics of solving problems on reactant excess and deficiency
- Organoleptic properties of solutions and identification of salt impurities
- Calculation of the number of atoms of complex composition in multicomponent molecules
- Analysis of double-replacement reaction equations with precipitate formation
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