Help with this Chemistry Question

Question

Hydrogen gas can be collected from the reaction of a metal element with a strong acid as

shown. When a 500.0 mg iron metal sample was soaked in 50.00 mL 0.500 M HNO3, 16.00 mg H2

was collected. How efficient is this process?

2Fe + 6HNO₃ → 2Fe(NO₃)₃ + 3H₂

Answer 1

2Fe + 6HNO₃ → 2Fe(NO₃)₃ + 3H₂ ... balanced equation

In asking how efficient the system is, they are essentially asking us to find the % yield and compare that to 100% yield.

To find % yield we need to find the theoretical yield first. To find theoretical yield, we need to find which reactant is limiting. An easy way to do this is to divide the mols of each reactant by the corresponding coefficient in the balanced equation.

For Fe: 500.0 mg Fe x 1 g/1000 mg x 1 mol/55.85 g = 0.00895 mols (÷2 -> 0.00448)

For HNO₃: 50.00 ml x 1 L/1000 ml x 0.500 mol/L = 0.025 mols (÷6 -> 0.00417)

The HNO₃ is limiting and will determine the theoretical yield of H₂ gas.

Theoretical yield:

0.025 mol HNO₃ x 3 mols H₂ / 6 mols HNO₃ x 2 g H₂ / mol x 1000 mg/g = 25.0 mg H₂ gas

% yield:

16.00 mg / 25.0 mg (x100%) = 64.0% This would be the efficiency of the process.