# Calculating Masses of Products

To find the mass of a product, first convert the mass of the given reactant to moles. Then, use the mole ratio from the balanced chemical equation to convert moles of the reactant to moles of the product. Finally, change the mole of the product to grams.

One of the major applications of the mole-mass conversion is calculating the product amounts from a balanced chemical equation. A balanced equation provides only the number of moles of reactants and the number of moles of products. The ratio between the number of moles of any two substances in a chemical reaction is called the mole ratio. In a laboratory, the mass of a substance is measured, not the number of moles, so converting from moles to mass is of great importance.

Consider the calculation of the amount of product from a reaction for which the masses are given. There are four steps to follow.

1. Write the balanced chemical equation for the reaction.
2. Find the number of moles of the reactants.
3. Calculate the number of moles of the products using the mole ratio from the balanced chemical equation.
4. Convert the number of moles of the products into mass.

Step-By-Step Example
Calculating Product Mass When Reactant Mass is Given
What mass of sodium sulfate (Na2SO4) is produced when 6.8 g of sodium hydroxide (NaOH) reacts with sulfuric acid (H2SO4)?
Step 1
Write the balanced equation.
$2\rm{NaOH}+{\rm H}_2{\rm{SO}}_4\rightarrow{\rm{Na}}_2{\rm{SO}}_4+2{\rm H}_2\rm O$
Step 2

Convert the given mass to moles.

First, determine the molar mass of NaOH using the atomic mass of each element from the periodic table.
\begin{aligned}{\text{Molar mass of }{\rm NaOH}}& = (1)(22.99{\rm{\; g/mol}})+(1)(16.00{\rm{\; g/mol}})+(1)(1.01{\rm{\; g/mol}})\\&= 40.00{\rm{\; g/mol}}\end{aligned}
Then, divide the given mass by the molar mass to convert to moles.
\begin{aligned}{{\text{Moles of }{\rm NaOH}}}&=\frac{{\text{Mass of }{\rm NaOH}}}{{\text{Molar mass of }{\rm NaOH}}}\\&= \frac{6.8{\rm{\; g}}}{40.00{\rm{\; g/mol}}}\\& = 0.17{\rm{\; mol\; NaOH}}\end{aligned}
Step 3
Use the coefficients of the balanced equation to determine the number of moles of the products that form.
\begin{aligned}{{\text{Moles of }{\rm Na_{2}SO}}}_4&=(0.17{\rm{\; mol\; NaOH}})\!\left( {\frac{1{\rm{\; mol\; Na}_2{\rm{SO}}_4}}{2{\rm{\; mol\; NaOH}}}} \right)\\& = 0.085{\rm{\; mol\; Na}}_2{\rm{SO}}_4\end{aligned}
Step 4
Determine the molar mass of Na2SO4 using the atomic mass of each element from the periodic table.
\begin{aligned}{{\text{Molar mass of }{\rm Na_{2}SO_{4}}}}& = (2)(22.99{\rm{\; g/mol}})+(1)(32.06{\rm{\; g/mol}})+(4)(16.00{\rm{\; g/mol}})\\&= 142.04{\rm{\; g/mol}}\end{aligned}
Solution
The mass of the product is the number of moles multiplied by the molar mass.
\begin{aligned}\text{Mass of }{\rm Na_{2}SO_{4}} &= ( 0.085{\rm{\; mol}})( 142.04{\rm{\; g/mol}}) \\&= 12{\rm{\; g\; Na}}_{2}{\rm{SO}}_{4}\end{aligned}
With the appropriate significant figures, the mass of Na2SO4 is 12 g.
Step-By-Step Example
Calculating Reactant Mass Required to Produce a Given Product Mass
Calculate the mass of sodium hydroxide (NaOH) required to produce 20.5 g of magnesium hydroxide, Mg(OH)2, when it reacts with magnesium chloride, MgCl2.
Step 1
Write the balanced equation for the reaction.
${\rm{MgCl}}_2+2\rm{NaOH}\rightarrow\rm{Mg}(\rm{OH})_2+2\rm{NaCl}$
Step 2
Calculate the molar mass of Mg(OH)2 using the number of each type of atom in the formula and the atomic mass of each element from the periodic table.
\begin{aligned}\text{Molar mass of }{\rm Mg(OH)_{2}}&=(1)(24.30\;\rm{g/mol})+(2)(16.00\;\rm{g/mol})+(2)(1.01\;\rm{g/mol})\\&=58.33\rm{\;g/mol}\end{aligned}
Step 3
Use the molar mass to convert the mass of Mg(OH)2 to number of moles of Mg(OH)2.
\begin{aligned}\text{Moles of }{\rm Mg(OH)_{2}}&=\frac{20.5\rm{\; g\; Mg(OH)}_2}{58.33\rm{\; g/mol}}\\&=0.3514\rm{\; mol\; Mg(OH)}_2\end{aligned}
An extra digit is included in the answer because this is an intermediate calculation.
Step 4
Use the coefficients of the balanced equation to convert moles of Mg(OH)2 to moles of NaOH.
\begin{aligned}\text{Moles of }{\rm NaOH}&=\left(0.3514\rm{\; mol\; Mg(OH)}_2\right)\!\left(\frac{1\;\rm {mol\; NaOH}}{1\rm{\; mol\; Mg(OH)}_2}\right)\\&=0.7028\rm{\; mol\; NaOH}\end{aligned}
Step 5
The molar mass of NaOH is needed in order to find the mass. Use the periodic table to determine the atomic mass of each atom. Then, multiply the corresponding molar mass of each atom by the number of atoms shown in the formula for sodium hydroxide.
\begin{aligned}\text{Molar mass of }{\rm NaOH}&=(1)(24.30\;\rm{g/mol})+(2)(16.00\;\rm{g/mol})+(2)(1.01\;\rm{g/mol})\\&=58.33\;\rm{g/mol}\end{aligned}
Solution
Use the molar mass of NaOH to calculate the mass of NaOH, expressed to three significant figures.
\begin{aligned}\text{Mass of }{\rm NaOH}&=(\text{Moles of }{\rm NaOH})(\text{Molar mass of }{\rm NaOH})\\&=(0.7028\rm{\; mol})(58.33\rm{\; g/mol})\\&=41.0\rm{\; g}\end{aligned}