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 H_{2}(g) + N_{2}(g) → 2 NH_{3}(g).

Calculate:

a. the mass in grams of NH_{3} formed from the reaction of 64.0 g of N_{2}

b. the mass in grams of N_{2} required for form 1.00 kg of NH_{3}**Solution**

From the balanced equation, it is known that:

1 mol N_{2} ∝ 2 mol NH_{3}

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 N_{2} = 2(14.0 g) = 28.0 g

1 mol of NH_{3} 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 NH_{3} formed from 64.0 g of N_{2}:

mass NH_{3} = 64.0 g N_{2} x 1 mol N_{2}/28.0 g NH_{2} x 2 mol NH_{3}/1mol NH_{3} x 17.0 g NH_{3}/1 mol NH_{3}

mass NH_{3} = 77.7 g NH_{3}

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

(1) grams NH_{3} → moles NH_{3} (1 mol NH_{3} = 17.0 g NH_{3})

(2) moles NH_{3} → moles N_{2} (1 mol N_{2} ∝ 2 mol NH_{3})

(3) moles N_{2} → grams N_{2} (1 mol N_{2} = 28.0 g N_{2})

mass N_{2} = 1.00 x 10^{3} g NH_{3} x 1 mol NH_{3}/17.0 g NH_{3} x 1 mol N_{2}/2 mol NH_{3} x 28.0 g N_{2}/1 mol N_{2}

mass N_{2} = 824 g N_{2}**Answer**

a.

mass NH_{3} = 77.7 g NH_{3}

b. mass N_{2} = 824 g N_{2}

### 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.