We have the balanced equation and the moles of each product. The coefficients in the equation can be used as a conversion ratio to find the amount of products created from each product.
N2(g)+ 3H2(g) --> 2NH
Step 1. Convert each mole of product to the moles of reactant produced
For nitrogen, we see that 1 mol N = 2 mol NH. We can convert mol N by solving
3.86 mol N x 2 mol NH / 1 mol N = 7.72 mol NH
For hydrogen, 3 mols H makes 2 mol NH. To convert mols H we can solve
6.70 mol H x 2 mol NH / 3 mol H = 4.47 mol NH
Step 2. Determine the limiting reactant. This is chosen based on which makes the least amount of product. In our case, this is hydrogen. Once the hydrogen is done reacting, there is no way more NH can be made. Based on this reasoning, we know that the amount of ammonia made is 4.47 mol NH.
Step 3. Convert ammonia into mass. The units for mass is grams so we can use the molar mass to figure out how many grams are produced.
4.47 mol NH x 17.031 g NH / 1 mol NH = 76.129 g NH