# Chemical Calculations | General Chemistry 2

## Mass-Mole-Number Relationship

**Mole number n (in mol):**

The number of moles in a sample

$\mathrm{n}=\frac{\mathrm{m}}{\mathrm{M}}$

m = mass of the substance (in g)

M = molar mass of the substance (in g.mol^{-1})

$\mathrm{n}=\frac{\mathrm{N}}{{\mathrm{N}}_{\mathrm{A}}}$

N = number of particles in the substance

N_{A} = Avogadro’s number = 6.022 x 10^{23} mol^{-1}

Number of mole n in 2.0 g of N_{2}:n = $\frac{{\mathrm{m}}_{{\mathrm{N}}_{2}}}{{\mathrm{M}}_{{\mathrm{N}}_{2}}}$

m

_{N2}= 2.0 g

M_{N2}= 2 x M_{N}= 2 x 14.0 = 28.0 g.mol^{-1}⇒ n = $\frac{2.0}{28.0}$ = 7.1 x 10

^{-2}mol

Number of nitrogen atom N_{N}in 2.0 g of N_{2}:n = $\frac{{\mathrm{m}}_{{\mathrm{N}}_{2}}}{{\mathrm{M}}_{{\mathrm{N}}_{2}}}$ = $\frac{{\mathrm{N}}_{{\mathrm{N}}_{2}}}{{\mathrm{N}}_{\mathrm{A}}}$

m

_{N2}= 2.0 g

M_{N2 }= 28.0 g.mol^{-1}

N_{N2}= 2 x N_{N}

N_{A}= 6.022 x 10^{-23}mol^{-1}⇒ N

_{N2}= N_{A}x $\frac{{\mathrm{m}}_{\mathrm{N}2}}{{\mathrm{M}}_{\mathrm{N}2}}$ = 4.3 x 10^{22}atomsN

_{N}= 2 x N_{N2}= 8.6 x 10^{22}atoms

## Percent Composition by Mass

The percent composition by mass is the percent of the total mass contributed by each element of a compound. It is calculated as follows:

%X = n x $\frac{{\mathrm{M}}_{\mathrm{X}}}{{\mathrm{M}}_{\mathrm{compound}}}$ x 100%

%X = percent composition of X

n = number of atoms X in a molecule of the compound

M_{x} = atomic mass of X (in amu or g.mol^{-1})

M_{compound} = molecular mass of the compound (in amu or g.mol^{-1})

Determine %Al in Al_{2}(SO_{4})_{3}:%Al = n x $\frac{{\mathrm{M}}_{\mathrm{Al}}}{{\mathrm{M}}_{{\mathrm{Al}}_{2}{\left({\mathrm{SO}}_{4}\right)}_{3}}}$ x 100%

n = 2 [2 atoms of Al in one molecule of Al

_{2}(SO_{4})_{3}]

M_{Al}= 26.98 g.mol^{-1}

M_{Al2(SO4)3}= 2 M_{Al }+ 3 M_{S}+ 12 M_{O}= 342.14 g.mol^{-1}%Al = 2 x $\frac{26.98}{342.14}$ x 100 = 15.77 %

## Stoichiometry

**Stoichiometric coefficients:**

The numeric values written to the left of each species in a chemical equation to balance the equation. The stoichiometric coefficients can be interpreted as the number of molecules or the number of moles of a substance produced or consumed during the reaction

3 H

_{2}+ N_{2}→ 2 NH_{3}Molecular interpretation: 3 molecules of H

_{2}react with 1 molecule of N_{2}to form 2 molecules of NH_{3}

Molar interpretation: 3 moles of H_{2}react with 1 mole of N_{2}to form 2 moles of NH_{3}

**Stoichiometry:**

The** **calculations of the masses, moles, or volumes of reactants and products involved in a chemical reaction. Reactants are said to be in stoichiometric amounts when their are combined in the same relative amounts as those represented in the balanced chemical equation

Stoichiometry problems:

- How much of a product can be formed starting from a certain amount of reactants
- How much of one reactant is necessary to react with a given amount of another
- How much reactant is required to produce a desired amount of product

**How to solve stoichiometry problems:**

- Balancing the chemical equation
- Calculate the molar masses of reactants and products of interest
- Convert all given masses to moles
- Use the balanced equation to determine the stoichiometric ratios
- Calculate the number of moles of desired materials
- Calculate the masses of desired materials

## Limiting Reactant

**Limiting reactant:**

The reactant that is consumed completely in a chemical reaction. The limiting reactant determines the maximum amount of product that can be formed during a reaction

**How to determine the limiting reactant:**

a A + b B → c C

- Consider one of the starting reagents as the limiting reactant (for example A)
- Calculate the mole number of the other reagent, B, required for a complete reaction of A

Be sure to use the stoichiometric ratios of the balanced equation: $\frac{{\mathrm{n}}_{\mathrm{A}}}{\mathrm{a}}$ = $\frac{{\mathrm{n}}_{\mathrm{B}}}{\mathrm{b}}$ - Compare the amount of B needed for a complete reaction with the actual amount of B:

If amount of B needed > actual amount of B, B is the limiting reactant

If actual amount of B > amount of B needed, A is the limiting reactant

## Percent Yield

**Theoritical vs. actual yield:**

Theoritical yield: the amount of product that will form if all the limiting reactant is consumed

Actual yield: the amount of product actually recovered

**Percent yield:**

A measure of the efficiency of a chemical reaction. The percent yield is calculated as follows:

% yield = $\frac{\mathrm{actual}\mathrm{yield}}{\mathrm{theoretical}\mathrm{yield}}$ x 100

### Check your knowledge about this Chapter

A mole is a fundamental unit in chemistry that represents a specific number of particles. It is important because it allows chemists to convert between the mass of a substance and the number of particles contained in that mass. Specifically, one mole is defined as 6.022 x 10^{23} particles, which is known as Avogadro's number.

The molar mass of a compound is calculated by adding the atomic masses of all the atoms in the compound's formula. The mass of each atom, taken from the periodic table, is multiplied by the number of times that atom occurs in the molecule.

The relationship between the mass of a substance and the amount in moles is quantified by the molar mass (in g/mol), which is the mass in grams of one mole of the substance. To determine the number of moles from mass, you divide the mass of the substance by its molar mass, and to convert moles to mass, you multiply the number of moles by the molar mass.

To convert between the number of particles (atoms, molecules) and moles, you use Avogadro's number, which is 6.022 x 10^{23} particles per mole. If you know the number of particles in a sample, you can divide by Avogadro's number to find the number of moles. Conversely, to find the number of particles from the number of moles, you multiply the moles by Avogadro's number.

Percent composition by mass refers to the percentage by mass of each element within a compound. To calculate it, one needs to divide the mass of each element in a molecule by the total molecular mass and then multiply by 100%. This calculation gives the contribution of each element to the overall mass of the molecule and is often used to determine the empirical formula or assess the purity of a compound.

The coefficients in chemical equations directly represent the stoichiometric ratios of reactants and products in a reaction. They indicate the proportionate amounts of substances involved when using the mole unit.

In the balanced chemical equation: 2 H

_{2}+ O_{2}→ 2 H_{2}O, the coefficients suggest that:2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This means that for every mole of oxygen consumed, twice as many moles of hydrogen are needed, and two moles of water are formed.

To perform a stoichiometric calculation in a chemical reaction, follow these steps:

- First, write down the balanced chemical equation for the reaction.
- Calculate the molar masses of the reactants and products.
- Convert the masses of the substances involved in the reaction to moles using their molar masses.
- Using the coefficients from the balanced equation, relate the moles of one substance to the moles of another substance.
- Identify the limiting reactant to determine the amount of products formed.
- Calculate the theoretical yield based on the moles of the limiting reactant and the mole ratio of the desired product to the limiting reactant.
- If given experimental data, calculate the percent yield by comparing the actual yield to the theoretical yield.

Stoichiometry is used to calculate the amount of product formed from the reactants by following these steps:

- Write the balanced chemical equation for the reaction.
- Convert the quantities of known substances (reactants or products) into moles using their molar masses.
- Use the mole ratio from the balanced equation to determine the number of moles of product that can form from the moles of reactant available.
- Convert the moles of product to grams (or another unit of measure) using the molar mass of the product.

This process relies on the law of conservation of mass and the principle that mole ratios in a balanced equation imply proportional relationships between reactants and products.

A limiting reactant is the reactant in a chemical reaction that is completely consumed first, thus limiting the extent of the reaction and determining the maximum amount of product that can be formed. The reaction stops when the limiting reactant is consumed, regardless of the amounts of other reactants present.

By comparing the mole ratio of the reactants used to the mole ratio of the reactants required by the balanced chemical equation, you can determine which reactant is the limiting one. Once identified, it is then used to calculate the theoretical yield of the product(s), knowing that no further product can form once the limiting reactant is expended.

To identify the limiting reactant in a chemical reaction, compare the molar ratios of the reactants used with those required by the balanced chemical equation:

- First, calculate the moles of each reactant present.
- Then, using the stoichiometry of the balanced equation, determine the amount of product(s) that each reactant could theoretically produce.
- The reactant that produces the least amount of product is the limiting reactant, as it will be consumed first, stopping the reaction, and therefore determining the maximum amount of product that can be formed.

Percent yield is calculated by dividing the actual yield (the experimentally obtained amount of product) by the theoretical yield (the maximum possible amount predicted by stoichiometry) and multiplying by 100.

#### Can you explain the concept of theoretical yield and its significance in percent yield calculations?

Theoretical yield is the maximum amount of product that could be formed in a reaction under ideal conditions. Percent yield relates the actual yield to the theoretical yield, providing insight into the efficiency of the reaction.

Factors that contribute to a lower than expected percent yield include incomplete reactions, side reactions, loss during transfer, and contaminants in the product.