Stoichiometry and Mole Ratios
Stoichiometry and Balanced Equations
Stoichiometry is a branch of chemistry that deals with the quantitative relationship between reactants and products in a Balanced Equation. Using the balanced chemical equation along with knowledge of atomic mass, molecular mass, the mole, Avogadro's number, and molar volume, we can calculate the amounts of substances involved in a reaction.
Law of Conservation of Mass: Stoichiometric calculations obey this law — total mass of reactants equals total mass of products
Law of Definite Proportions: Also obeyed — a given compound always contains its constituent elements in a fixed ratio by mass
Assumptions: All reactants are completely converted into products, and no side reactions occur
A balanced chemical equation enables several types of quantitative calculations between reactants and products. Each type connects different ways of expressing amount — mass, moles, volume, and number of particles.
Mass-Mass Relationship: Given the mass of one substance, calculate the mass of any other substance in the reaction
Mole-Mole Relationship: Given the moles of one substance, calculate the moles of another using the coefficients from the balanced equation
Mass-Volume Relationship: Given the mass of one substance, calculate the volume of another (or vice versa), using density to convert between mass and volume
Types of Stoichiometric Relationships
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Mass ↔ Mass: convert given mass to moles, apply mole ratio, convert result back to mass
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Mass ↔ Moles: convert given mass to moles (or vice versa), apply mole ratio for the other substance
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Mass ↔ Volume: convert given mass to moles, apply mole ratio, convert to mass, then use density to find volume
Constructing Mole Ratios from Balanced Equations
The coefficients in a Balanced Equation represent the relative number of moles of each substance involved in the reaction. A Mole Ratio is the ratio of these coefficients and is used as a conversion factor to relate the amounts of any two substances in the reaction.
$$2KOH + H_2SO_4 \longrightarrow K_2SO_4 + 2H_2O$$
The coefficients (2, 1, 1, 2) tell us that 2 moles of KOH react with 1 mole of H2SO4 to produce 1 mole of K2SO4 and 2 moles of H2O
$2$=moles of KOH consumed(mol)
$1$=moles of H2SO4 consumed(mol)
$1$=moles of K2SO4 produced(mol)
$2$=moles of H2O produced(mol)
any pair of substances
→a mole ratio can be written as the ratio of their coefficients, e.g. KOH:K2SO4 = 2:1, KOH:H2O = 2:2 = 1:1
Reading Mole Ratios Directly: From the balanced equation, the coefficient ratio of KOH to K2SO4 is 2:1 — every 2 moles of KOH produce exactly 1 mole of K2SO4
Simplifying Ratios: Mole ratios can be simplified like fractions — the ratio KOH:H2O = 2:2 simplifies to 1:1, meaning equal moles
Cross-Substance Ratios: Ratios are not limited to reactant-product pairs — you can write a ratio between any two substances, such as K2SO4:H2O = 1:2
To construct and apply a Mole Ratio, follow a systematic approach: identify the given substance and the target substance from the balanced equation, write their coefficient ratio, then use it to convert moles of the given substance to moles of the target.
Step 1 — Identify Substances: Locate both the given substance and the target substance in the balanced equation
Step 2 — Write Coefficient Ratio: Extract the coefficients of both substances and write them as a ratio (target : given)
Step 3 — Multiply: Multiply the known moles of the given substance by this ratio to get the moles of the target substance
Mole Ratios from $2KOH + H_2SO_4 \rightarrow K_2SO_4 + 2H_2O$
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KOH : K2SO4 = 2 : 1
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KOH : H2O = 2 : 2 = 1 : 1
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H2SO4 : K2SO4 = 1 : 1
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H2SO4 : H2O = 1 : 2
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K2SO4 : H2O = 1 : 2
Stoichiometric Calculations Using Balanced Equations
Most stoichiometric calculations follow a three-step process: convert the given quantity to moles, use the Mole Ratio from the balanced equation to find moles of the target substance, then convert the result to the desired unit. This framework works for mass-mass, mole-mole, and mass-volume calculations alike.
$$n = \frac{m}{M}$$
Converts between mass and moles — dividing mass by molar mass gives the number of moles
$n$=number of moles(mol)
$m$=mass of the substance(g)
$M$=molar mass of the substance(g/mol)
converting moles to number of particles
→multiply moles by Avogadro's number ($6.02 \times 10^{23}$ mol$^{-1}$)
converting moles back to mass
→multiply moles by molar mass: $m = n \times M$
Step 1 — Convert to Moles: If the given quantity is a mass, divide by molar mass to get moles. If already in moles, proceed directly to Step 2
Step 2 — Apply Mole Ratio: Use the coefficients from the balanced equation to convert moles of the given substance to moles of the target substance
Step 3 — Convert to Desired Unit: Convert the resulting moles to mass (× molar mass), volume (÷ density), or number of particles (× Avogadro's number)
Three-Step Stoichiometric Method
1
Given quantity → Moles (using molar mass or Avogadro's number)
2
Moles of given → Moles of target (using mole ratio from balanced equation)
3
Moles of target → Desired quantity (mass, volume, or particle count)
In a mass-mass calculation, the mass of one substance is given and the mass of another substance must be determined. This requires converting the given mass to moles, applying the Mole Ratio, and converting the resulting moles back to mass using the Molar Mass of the target substance.
$$m_{\text{target}} = m_{\text{given}} \times \frac{1}{M_{\text{given}}} \times \frac{c_{\text{target}}}{c_{\text{given}}} \times M_{\text{target}}$$
Combines all three steps into one expression: convert given mass to moles, apply mole ratio, convert back to mass
$m_{\text{given}}$=mass of the given substance(g)
$M_{\text{given}}$=molar mass of the given substance(g/mol)
$c_{\text{target}}$=coefficient of the target substance in the balanced equation(dimensionless)
$c_{\text{given}}$=coefficient of the given substance in the balanced equation(dimensionless)
$M_{\text{target}}$=molar mass of the target substance(g/mol)
$c_{\text{target}} = c_{\text{given}}$
→the mole ratio is 1:1 and cancels out — moles are equal, so only molar masses matter
Given Mass to Given Moles: Divide the given mass by the molar mass of the given substance
Given Moles to Target Moles: Multiply by the ratio (target coefficient / given coefficient)
Target Moles to Target Mass: Multiply the target moles by the molar mass of the target substance
When the target substance is a solution with known percentage concentration and density, additional conversion steps are needed after finding the moles of solute. The percentage by weight relates the mass of solute to the total mass of solution, and density relates the solution mass to its volume.
$$V = \frac{m_{\text{solute}}}{\% \times \rho}$$
Converts mass of solute to volume of solution by accounting for concentration (percentage) and density
$V$=volume of the solution(cm³)
$m_{\text{solute}}$=mass of the solute (pure substance)(g)
$\%$=percentage concentration by weight (expressed as a decimal, e.g. 27% = 0.27)(dimensionless)
$\rho$=density of the solution(g/cm³)
$\% = 1$ (100% pure substance)
→the formula reduces to $V = m / \rho$, the standard density formula
From Moles to Solute Mass: After finding moles of solute via mole ratio, multiply by its molar mass to get the mass of pure solute needed
From Solute Mass to Solution Mass: Divide the solute mass by the percentage concentration (as a decimal) to get the total mass of solution
From Solution Mass to Volume: Divide the solution mass by the density of the solution to obtain the volume required
Calculation Sequence for Solution-Based Problems
1
Given mass of product → moles of product (÷ molar mass of product)
2
Moles of product → moles of solute (× mole ratio from balanced equation)
3
Moles of solute → mass of solute (× molar mass of solute)
4
Mass of solute → mass of solution (÷ percentage concentration as decimal)
5
Mass of solution → volume of solution (÷ density of solution)