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...

##2.24 "L"##

Step 1: determine the reaction

The chemical equation is already given.

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

Step 3: determine how much ##"H"_2## is produced.

##0.100 "mol"## of ##"Mg"## and ##0.200 "mol"## of ##"HCl"## will produce ##0.100 "mol"## of ##"H"_2##.

Step 4: determine the volume at STP

Each mole of ideal gas occupies ##22.4 "L"## at STP. Therefore, ##0.100 "mol"## of ##"H"_2## will occupy ##2.24 "L"## of space.