# Lithium and nitrogen react to produce lithium nitride: 6Li(s) + N_2(g) -> 2Li_3N(s). How many moles of lithium nitride are produced when 0.710 mol of lithium react in this fashion?

Mar 5, 2017

We will obtain 0.237 mol of $L {i}_{3} N$

#### Explanation:

Since the given information is in moles, we need only look at the ratio between the chemicals:

Six moles of Li will produce 2 moles of lithium nitride. So, the ratio is 6:2 or 3:1.

Therefore, we can set up a proportion:

$\frac{L i}{L {i}_{3} N} = \frac{3}{1} = \frac{0.710}{x}$

This tells us that in the general case, we need three times as much Li as the amount of $L {i}_{3} N$ to be produced, and that the amount of $L {i}_{3} N$ produced in this case must be in the same ratio. so, we can solve

$\frac{3}{1} = \frac{0.710}{x}$

Cross-multiply

$3 x = 0.710$

$x = 0.710 \div 3 = 0.237$ mol of $L {i}_{3} N$ produced