**Given:** Volume of #"H"_2# at STP; #P# and #T# of #"HCl"#; chemical equation (understood)

**Find:** Volume of #"HCl"#

**Strategy:**

The central part of any stoichiometry problem is to **convert moles of something to moles of something else**.

**(a)** We start with the balanced chemical equation for the reaction.

**(b)** We can use the **molar ratio** from the equation to convert moles of #"H"_2# to moles of #"HCl"#.

#"moles of H"_2stackrelcolor (blue)("molar ratio"color(white)(Xl))( →) "moles of HCl"#

**(c)** We can use the **Ideal Gas Law** (IGL) to convert the volume of #"H"_2# to moles of #"H"_2#.

**(d)** We can also use the IGL to convert moles of #"HCl"# to volume of #"HCl"#.

Our complete strategy is:

#"Volume of H"_2stackrelcolor (blue)("IGL"color(white)(Xl))(→) "moles of H"_2stackrelcolor (blue)("molar ratio"color(white)(Xl))( →) "moles of HCl"stackrelcolor (blue)( "IGL"color(white)(Xl))(→)"Volume of HCl"#

**Solution**

**(a)** The balanced equation is

#"H"_2 + "Cl"_2 → "2HCl"#

**(b)** Calculate moles of #"H"_2#

STP is defined as #10^5color(white)(l) "Pa"# and #"273.15 K"#.

#PV = nRT#

#n = (PV)/(RT) = (10^5 color(red)(cancel(color(black)("Pa"))) × 1150 color(red)(cancel(color(black)("m"^3))))/(8.314 color(red)(cancel(color(black)("Pa·m"^3"K"^(-1))))"mol"^(-1) × 273.15 color(red)(cancel(color(black)("K")))) = "50 640 mol"#

**(c)** Calculate moles of #"HCl"#

The molar ratio of #"HCl to H"_2# is #"2 mol HCl"/("1 mol H"_2)"#

#"Moles of HCl" = 50 640 color(red)(cancel(color(black)("mol H"_2))) × "2 mol HCl"/(1 color(red)(cancel(color(black)("mol H"_2)))) = "101 280 mol HCl"#

**(d)** Calculate the volume of #"HCl"#

#105 color(red)(cancel(color(black)("kPa"))) × "1000 Pa"/(1 color(red)(cancel(color(black)("kPa")))) = "105 000 Pa"#

#PV = nRT#

#V= (nRT)/P = ("101 280" color(red)(cancel(color(black)("mol"))) × 8.314 color(red)(cancel(color(black)("Pa")))"·m"^3color(red)(cancel(color(black)("K"^(-1)"mol"^(-1)))) × 296 color(red)(cancel(color(black)("K"))))/("105 000" color(red)(cancel(color(black)("Pa")))) = "2370 m"^3#

(3 significant figures)

**Answer:** The reaction will form #"2370 m"^3# of #"HCl"#.