8.5: Mass-to-Mass Conversions

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⚙️ Learning Objectives

Convert from mass or moles of one substance to mass or moles of another substance in a chemical reaction.

Mole-to-Mass Conversions

We have established that a balanced chemical equation is balanced in terms of moles, as well as atoms or molecules. We have used balanced equations to set up ratios, in terms of moles of materials, that we can use as conversion factors to answer stoichiometric questions – such as how many moles of substance A react with so many moles of reactant B. We can extend this technique even further. Recall that we can relate a molar amount to a mass amount using molar mass. We can use that relation to answer stoichiometry questions in terms of the masses of a particular substance, in addition to moles. We do this using the following sequence:

\({\color[rgb]{0.8, 0.0, 0.0}\boxed{\;\mathrm{moles}\;\mathrm{of}\;\mathrm A\;}}\;\xrightarrow[\mathrm{ratio}]{\mathrm{molar}}\;{\color[rgb]{0.0, 0.0, 1.0}\boxed{\;\mathrm{moles}\;\mathrm{of}\;\mathrm B\;}}\;\xrightarrow[\mathrm{mass}]{\mathrm{molar}}\;{\color[rgb]{0.0, 0.5, 0.0}\boxed{\;\mathrm{grams}\;\mathrm{of}\;\mathrm B\;}}\)

Collectively, these conversions are called mole-to-mass calculations. As an example, consider the balanced chemical equation

Fe₂O₃ + 3 SO₃ → Fe₂(SO₄)₃

Suppose we wanted to know how many grams of SO₃ will react with 3.59 mol of Fe₂O₃. Using the mole-mass calculation sequence, we can determine the required mass of SO₃ in two steps. First, we construct the appropriate molar ratio, determined from the balanced chemical equation, to calculate the number of moles of SO₃ needed. From here, the mass of SO₃ may be calculated using the molar mass of SO₃ as a conversion factor.

Relationship		Possible Conversions
molar ratio	1 mol Fe₂O₃: 3 mol SO₃	\(\dfrac{1\;\mathrm{mol}\;{\mathrm{Fe}}_2{\mathrm O}_3}{3\;\mathrm{mol}\;{\mathrm{SO}}_3}\) or \(\dfrac{3\;\mathrm{mol}\;{\mathrm{SO}}_3}{1\;\mathrm{mol}\;{\mathrm{Fe}}_2{\mathrm O}_3}\)
molar mass	1 mol SO₃ = 80.07 g SO₃	\(\dfrac{80.07\;\mathrm g\;{\mathrm{SO}}_3}{1\;\mathrm{mol}\;{\mathrm{SO}}_3}\) or \(\dfrac{1\;\mathrm{mol}\;{\mathrm{SO}}_3}{80.07\;\mathrm g\;{\mathrm{SO}}_3}\)

As before, start with the quantity given (3.59 mol Fe₂O₃):

\(3.59\:\cancel{\mathrm{mol}\:{\mathrm{Fe}}_2{\mathrm O}_3}\times\dfrac{3\:\mathrm{mol}\:{\mathrm{SO}}_3}{1\:\cancel{\mathrm{mol}\:{\mathrm{Fe}}_2{\mathrm O}_3}}=10.\underline77\:\mathrm{mol}\:{\mathrm{SO}}_3\)

Moles of Fe₂O₃ cancel, leaving moles of SO₃ as the units. This answer may then be converted to grams of SO₃:

\(10.\underline77\;\cancel{\mathrm{mol}\;{\mathrm{SO}}_3}\times\dfrac{80.07\:\mathrm g\:{\mathrm{SO}}_3}{1\;\cancel{\mathrm{mol}\;{\mathrm{SO}}_3}}=\boxed{862\:\mathrm g\:{\mathrm{SO}}_3}\)

The final answer is expressed to three significant figures. Thus, in a two-step process, we find that 862 g of SO₃ will react with 3.59 mol of Fe₂O₃. Many problems of this type can be answered in this manner. It is generally easier if the problem is set up in a single series of steps:

\(3.59\cancel{\,\mathrm{mol}\,{\mathrm{Fe}}_2{\mathrm O}_3}\times\dfrac{3\;\cancel{\mathrm{mol}\;{\mathrm{SO}}_3}}{1\;\cancel{\mathrm{mol}\;{\mathrm{Fe}}_2{\mathrm O}_3}}\times\dfrac{80.07\;\mathrm g\;{\mathrm{SO}}_3}{1\;\cancel{\mathrm{mol}\;{\mathrm{SO}}_3}}=\boxed{862\,\mathrm g\,{\mathrm{SO}}_3}\)

Notice that the identical answer is obtained, in much the same manner as when multi-step dimensional analysis was introduced in Section 2.7.

✅ Example \(\PageIndex{1}\): Generation of Aluminum Oxide

How many moles of HCl will be produced when 249 g of AlCl₃ are reacted according to this chemical equation?

2 AlCl₃ + 3 H₂O → Al₂O₃ + 6 HCl

Solution

Steps for Problem Solving
Identify the "given" information and what the problem is asking you to "find."	Given: 249 g AlCl₃ Find: moles HCl
List other known quantities.	1 mol AlCl₃ = 133.33 g AlCl₃ 2 mol AlCl₃: 6 mol HCl
Prepare a concept map using the proper conversion factor(s).	\({\color[rgb]{0.8, 0.0, 0.0}\boxed{\;\;\mathrm g\;{\mathrm{AlCl}}_3\;\;}}\xrightarrow[{133.33\;\mathrm g\;{\mathrm{AlCl}}_3}]{1\;\mathrm{mol}\;{\mathrm{AlCl}}_3}{\color[rgb]{0.0, 0.0, 1.0}\boxed{\mathrm{mol}\;{\mathrm{AlCl}}_3}}\xrightarrow[{2\;\mathrm{mol}\;{\mathrm{AlCl}}_3}]{6\;\mathrm{mol}\;\mathrm{HCl}}{\color[rgb]{0.0, 0.5, 0.0}\boxed{\;\mathrm{mol}\;\mathrm{HCl}\;}}\)
Cancel units and calculate.	\(249\;\cancel{\mathrm g\;{\mathrm{AlCl}}_3}\times\dfrac{1\;\cancel{\mathrm{mol}\;{\mathrm{AlCl}}_3}}{133.33\;\,\cancel{\mathrm g\;{\mathrm{AlCl}}_3}}\times\dfrac{6\;\mathrm{mol}\,\mathrm{HCl}}{2\;\cancel{\mathrm{mol}\,{\mathrm{AlCl}}_3}}=\boxed{5.60\;\mathrm{mol}\;\mathrm{HCl}}\)
Think about your result.	249 g AlCl₃ is less than 266.66 g (the mass for 2 mol AlCl₃). Since the relationship is 6 mol HCl to 2 mol AlCl₃, the answer should be less than 6 mol HCl. The answer of 5.60 mol HCl is indeed less than 6 mol HCl.

✏️ Exercise \(\PageIndex{1}\): Generation of Aluminum Oxide

How many moles of Al₂O₃ will be produced when 23.9 g of H₂O are reacted according to this chemical equation?

2 AlCl₃ + 3 H₂O → Al₂O₃ + 6 HCl

Answer: 0.442 mol Al₂O₃

Mass-to-Mass Conversions

In the real world, the number of molecules or moles are not measured directly. Rather, it is the masses of the reactants and/or products that will be measured directly. Consequently, it is much more practical to make all measurements in terms of the number of grams. It is a small step to move from mole-to-mass calculations to mass-to-mass calculations.

If we start with a known mass of one substance in a chemical reaction (instead of a known number of moles), we can calculate the corresponding masses of other substances in the reaction. The first step in this case is to convert the known mass into moles, using the substance’s molar mass as the conversion factor. Then – and only then – the balanced chemical equation is used to construct a conversion factor to convert that quantity to moles of another substance, which in turn can be converted to a corresponding mass. Sequentially, the process is as follows:

\({\color[rgb]{0.5, 0.0, 0.5}\boxed{\;\mathrm{grams}\;\mathrm{of}\;\mathrm A\;}}\xrightarrow[\mathrm{mass}]{\mathrm{molar}}{\color[rgb]{0.8, 0.0, 0.0}\boxed{\;\mathrm{moles}\;\mathrm{of}\;\mathrm A\;}}\xrightarrow[\mathrm{ratio}]{\mathrm{molar}}{\color[rgb]{0.0, 0.0, 1.0}\boxed{\;\mathrm{moles}\;\mathrm{of}\;\mathrm B\;}}\xrightarrow[\mathrm{mass}]{\mathrm{molar}}{\color[rgb]{0.0, 0.5, 0.0}\boxed{\;\mathrm{grams}\;\mathrm{of}\;\mathrm B\;}}\)

This three-part process can be carried out in three discrete steps or combined into a single calculation that contains three conversion factors. This text will generally approach this type of problem in a single series of steps.

✅ Example \(\PageIndex{2}\): Decomposition of Ammonium Nitrate

Ammonium nitrate decomposes to dinitrogen monoxide and water according to the following equation.

NH₄NO₃ (s) → N₂O (g) + 2 H₂O (l)

Find the mass of each product formed when 45.7 g of ammonium nitrate is decomposed.

Solution

Steps for Problem Solving
Identify the "given" information and what the problem is asking you to "find."	Given: 45.7 g NH₄NO₃ Find: Mass N₂O, Mass H₂O
List other known quantities.	1 mol NH₄NO₃ = 80.05 g NH₄NO₃ 1 mol N₂O = 44.02 g N₂O 1 mol H₂O = 18.02 g H₂O 1 mol NH₄NO₃: 1 mol N₂O 1 mol NH₄NO₃: 2 mol H₂O
Prepare concept maps using the proper conversion factor(s).	\({\color[rgb]{0.5, 0.0, 0.5}\boxed{\;\;\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3\;\;}}\xrightarrow[{80.05\;\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3}]{1\;\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}{\color[rgb]{0.8, 0.0, 0.0}\boxed{\;\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3\;}}\xrightarrow[{1\;\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}]{1\;\mathrm{mol}\;{\mathrm N}_2\mathrm O}{\color[rgb]{0.0, 0.0, 1.0}\boxed{\;\;\;\mathrm{mol}\;{\mathrm N}_2\mathrm O\;\;\;}}\xrightarrow[{1\;\mathrm{mol}\;{\mathrm N}_2\mathrm O}]{44.02\;\mathrm g\;{\mathrm N}_2\mathrm O}{\color[rgb]{0.0, 0.5, 0.0}\boxed{\;\;\;\;\mathrm g\;{\mathrm N}_2\mathrm O\;\;\;\;}}\) \({\color[rgb]{0.5, 0.0, 0.5}\boxed{\;\;\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3\;\;}}\xrightarrow[{80.05\;\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3}]{1\;\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}{\color[rgb]{0.8, 0.0, 0.0}\boxed{\;\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3\;}}\xrightarrow[{1\;\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}]{2\;\mathrm{mol}\;{\mathrm H}_2\mathrm O}{\color[rgb]{0.0, 0.0, 1.0}\boxed{\;\;\;\mathrm{mol}\;{\mathrm H}_2\mathrm O\;\;\;}}\xrightarrow[{1\;\mathrm{mol}\;{\mathrm H}_2\mathrm O}]{18.02\;\mathrm g\;{\mathrm H}_2\mathrm O}{\color[rgb]{0.0, 0.5, 0.0}\boxed{\;\;\;\;\mathrm g\;{\mathrm H}_2\mathrm O\;\;\;\;}}\)
Cancel units and calculate.	\(45.7\:\cancel{\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3}\times\dfrac{1\;\cancel{\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}}{80.05\:\cancel{\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3}}\times\dfrac{1\;\cancel{\mathrm{mol}\;{\mathrm N}_2\mathrm O}}{1\:\cancel{\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}}\times\dfrac{44.02\;\mathrm g\;{\mathrm N}_2\mathrm O}{1\;\cancel{\mathrm{mol}\;{\mathrm N}_2\mathrm O}}=\boxed{25.1\;\mathrm g\;{\mathrm N}_2\mathrm O}\) \(45.7\:\cancel{\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3}\times\dfrac{1\;\cancel{\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}}{80.05\:\cancel{\mathrm g\;{\mathrm{NH}}_4{\mathrm{NO}}_3}}\times\dfrac{2\;\cancel{\mathrm{mol}\;{\mathrm H}_2\mathrm O}}{1\:\cancel{\mathrm{mol}\;{\mathrm{NH}}_4{\mathrm{NO}}_3}}\times\dfrac{18.02\;\mathrm g\;{\mathrm H}_2\mathrm O}{1\;\cancel{\mathrm{mol}\;{\mathrm H}_2\mathrm O}}=\boxed{20.6\;\mathrm g\;{\mathrm H}_2\mathrm O}\)
Think about your result.	The sum of the masses of the two products is equal to the mass of ammonium nitrate decomposed. This demonstrates the Law of Conservation of Mass. Each answer has three significant figures.

✏️ Exercise \(\PageIndex{2}\): Carbon Tetrachloride

Methane reacts with elemental chlorine to make carbon tetrachloride, CCl₄. The balanced chemical equation for this reaction is:

CH₄ (g) + 4 Cl₂ (g) → CCl₄ (l) + 4 HCl (g)

How many grams of HCl are produced by the reaction of 100.0 g CH₄?

Answer: 909.1 g HCl

✅ Example \(\PageIndex{3}\): Production of Ammonia

Taking into consideration the balanced chemical equation:

N₂ (g) + 3 H₂ (g) → 2 NH₃ (g)

what mass of hydrogen gas is needed to prepare 404 g of ammonia?

Solution

Steps for Problem Solving
Identify the "given" information and what the problem is asking you to "find."	Given: 404 g NH₃ Find: Mass H₂
List other known quantities.	1 mol NH3 = 17.03 g NH₃ 1 mol H₂ = 2.016 g H₂ 3 mol H₂: 2 mol NH₃
Prepare concept maps using the proper conversion factor(s).	\({\color[rgb]{0.5, 0.0, 0.5}\boxed{\;\;\mathrm g\;{\mathrm{NH}}_3\;\;}}\xrightarrow[{17.03\;\mathrm g\;{\mathrm{NH}}_3}]{1\;\mathrm{mol}\;{\mathrm{NH}}_3}{\color[rgb]{0.8, 0.0, 0.0}\boxed{\;\mathrm{mol}\;{\mathrm{NH}}_3\;}}\xrightarrow[{2\;\mathrm{mol}\;{\mathrm{NH}}_3}]{3\;\mathrm{mol}\;{\mathrm H}_2}{\color[rgb]{0.0, 0.0, 1.0}\boxed{\;\;\mathrm{mol}\;{\mathrm H}_2\;\;}}\xrightarrow[{1\;\mathrm{mol}\;{\mathrm H}_2}]{2.016\;\mathrm g\;{\mathrm H}_2}{\color[rgb]{0.0, 0.5, 0.0}\boxed{\;\;\;\;\mathrm g\;{\mathrm H}_2\;\;\;\;}}\)
Cancel units and calculate.	\(404\:\cancel{\mathrm g\;{\mathrm{NH}}_3}\times\dfrac{1\;\cancel{\mathrm{mol}\;{\mathrm{NH}}_3}}{17.03\:\cancel{\mathrm g\;{\mathrm{NH}}_3}}\times\dfrac{3\;\cancel{\mathrm{mol}\;{\mathrm H}_2}}{2\:\cancel{\mathrm{mol}\;{\mathrm{NH}}_3}}\times\dfrac{2.016\;\mathrm g\;{\mathrm H}_2}{1\;\cancel{\mathrm{mol}\;{\mathrm H}_2}}=\boxed{71.7\;\mathrm g\;{\mathrm H}_2}\)
Think about your result.	404 g NH₃ is a bit more than 20 mol N₃. Since the molar ratio is 3 mol H₂: 2 mol NH₃, a bit more than 30 mol H₂ are needed. 71.7 g H₂ is a bit more than 30 mol H₂.

✏️ Exercise \(\PageIndex{3}\): Vanadium(V) Oxide

Vanadium metal reacts with oxygen gas to yield solid vanadium(V) oxide:

4 V (s) + 5 O₂ (g) → 2 V₂O₅ (s)

What is the molar ratio between V and O₂?
How many moles of V will react with 9.25 mol O₂?
What mass of vanadium is needed to produce 0.301 g V₂O₅?

Answer A: 4 mol V: 5 mol O₂

Answer B: 7.40 mol V

Answer C: 0.169 g V

Summary

Calculations involving conversions between moles of a substance and the mass of that substance can be done using conversion factors.
A balanced chemical reaction can be used to determine molar and mass relationships between substances.

This page is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Lance S. Lund (Anoka-Ramsey Community College), Marisa Alviar-Agnew, and Henry Agnew.

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