# Magnesium metal (0.100 mol) and a volume of aqueous hydrochloric acid that contains 0.500 mol of HCl are combined and react to completion. How many liters of hydrogen gas, measured at STP, can be produced? "Mg"(s) + 2"HCl"(aq) -> "MgCl"_2(aq) + "H"_2(g)

May 7, 2016

$2.24 \text{L}$

#### Explanation:

Step 1: determine the reaction

The chemical equation is already given.

${\text{Mg" + 2 "HCl" -> "MgCl"_2 + "H}}_{2}$

Step 2: determine which reactant is limiting

0.100 mol of Mg reacts with 0.500 mol of HCl, which of them will run out first?

From the reaction, the ratio of $\text{Mg}$ to $\text{HCl}$ used is $1 : 2$. This means that if the reaction goes to completion, the $0.100 \text{mol}$ of $\text{Mg}$ will react with $0.100 \text{mol" xx 2 = 0.200 "mol}$ of $\text{HCl}$. This leaves $0.500 \text{mol" - 0.200 "mol" = 0.300 "mol}$ of $\text{HCl}$.

Step 3: determine how much ${\text{H}}_{2}$ is produced.

$0.100 \text{mol}$ of $\text{Mg}$ and $0.200 \text{mol}$ of $\text{HCl}$ will produce $0.100 \text{mol}$ of ${\text{H}}_{2}$.

Step 4: determine the volume at STP

Each mole of ideal gas occupies $22.4 \text{L}$ at STP. Therefore, $0.100 \text{mol}$ of ${\text{H}}_{2}$ will occupy $2.24 \text{L}$ of space.