# Mass Relations in Balanced Equations Example Problem

## Finding Mass of Reagents and Products

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. Here's how to find the mass of a compound from its equation, 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:
a. the mass in grams of NH3 formed from the reaction of 64.0 g of N2
b. 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) grams NH3 → moles NH3 (1 mol NH3 = 17.0 g NH3)

(2) moles NH3 → moles N2 (1 mol N2 ∝ 2 mol NH3)

(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

a.

mass NH3 = 77.7 g NH3
b. mass N2 = 824 g N2

### Tips for Finding Mass from Equations

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 to use the atomic masses for the elements with the same number of significant figures as you're given in your problem. Usually, this is 3 or 4 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.