Example Problem of Mass Relations in Balanced Equations

A mass relation refers to the ratio of the mass of reactants and products to each other. In a balanced chemical equation, you can use the mole ratio to solve for mass in grams. You can use an equation to learn how to find the mass of a compound, provided you know the quantity of any participant in the reaction.

Mass Balance Problem

The balanced equation for the synthesis of ammonia is 3 H₂(g) + N₂(g) → 2 NH₃(g).

Calculate:

1. The mass in grams of NH₃ formed from the reaction of 64.0 g of N₂
2. The mass in grams of N₂ required for form 1.00 kg of NH₃

Solution:

From the balanced equation, it is known that:

1 mol N₂ ∝ 2 mol NH₃

Use the periodic table to look at the atomic weights of the elements and calculate the weights of the reactants and products:

1 mol of N₂ = 2(14.0 g) = 28.0 g

1 mol of NH₃ is 14.0 g + 3(1.0 g) = 17.0 g

These relations can be combined to give the conversion factors needed to calculate the mass in grams of NH₃ formed from 64.0 g of N₂:

Mass NH₃ = 64.0 g N₂ x 1 mol N₂/28.0 g NH₂ x 2 mol NH₃/1mol NH₃ x 17.0 g NH₃/1 mol NH₃

Mass NH₃ = 77.7 g NH₃

To obtain the answer to the second part of the problem, the same conversions are used in a series of three steps:

1. (1) grams NH₃ → moles NH₃ (1 mol NH₃ = 17.0 g NH₃)
2. (2) moles NH₃ → moles N₂ (1 mol N₂ ∝ 2 mol NH₃)
3. (3) moles N₂ → grams N₂ (1 mol N₂ = 28.0 g N₂)

Mass N₂ = 1.00 x 10³ g NH₃ x 1 mol NH₃/17.0 g NH₃ x 1 mol N₂/2 mol NH₃ x 28.0 g N₂/1 mol N₂

Mass N₂ = 824 g N₂

Answer:

1. mass NH₃ = 77.7 g NH₃
2. mass N₂ = 824 g N₂

How to Calculate Grams With a Balanced Equation

If you're having trouble getting the correct answer for this type of problem, check the following:

• Make certain the chemical equation is balanced. If you're working from an unbalanced equation, the very first step is balancing it.
• Check to make sure you're converting between grams and moles correctly.
• You may be solving the problem correctly, but getting the wrong answer because you didn't work with the correct number of significant figures throughout the process. It's good practice using the atomic masses for the elements with the same number of significant figures as you're given in your problem. Usually, this is three or four significant figures. Using the "wrong" value can throw you off on the last decimal point, which will give you the wrong answer if you're entering it into a computer.
• Pay attention to the subscripts. For example, the grams to mole conversion for nitrogen gas (two nitrogen atoms) is different than if you had a single nitrogen atom.