# The hydrogen chloride gas used to make polyvinyl chloride plastic is made by reacting hydrogen gas with chlorine gas. What volume of HCL at 105 kPa and 296 K can be formed from 1150 m^3 of H_2 at STP?

Jan 9, 2016

The reaction will form ${\text{2370 m}}^{3}$ of $\text{HCl}$.

#### Explanation:

Given: Volume of ${\text{H}}_{2}$ at STP; $P$ and $T$ of $\text{HCl}$; chemical equation (understood)

Find: Volume of $\text{HCl}$

Strategy:

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

(b) We can use the molar ratio from the equation to convert moles of ${\text{H}}_{2}$ to moles of $\text{HCl}$.

$\text{moles of H"_2stackrelcolor (blue)("molar ratio"color(white)(Xl))( →) "moles of HCl}$

(c) We can use the Ideal Gas Law (IGL) to convert the volume of ${\text{H}}_{2}$ to moles of ${\text{H}}_{2}$.

(d) We can also use the IGL to convert moles of $\text{HCl}$ to volume of $\text{HCl}$.

Our complete strategy is:

$\text{Volume of H"_2stackrelcolor (blue)("IGL"color(white)(Xl))(→) "moles of H"_2stackrelcolor (blue)("molar ratio"color(white)(Xl))( →) "moles of HCl"stackrelcolor (blue)( "IGL"color(white)(Xl))(→)"Volume of HCl}$

Solution

(a) The balanced equation is

$\text{H"_2 + "Cl"_2 → "2HCl}$

(b) Calculate moles of ${\text{H}}_{2}$

STP is defined as ${10}^{5} \textcolor{w h i t e}{l} \text{Pa}$ and $\text{273.15 K}$.

$P V = n R T$

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 $\text{HCl}$

The molar ratio of ${\text{HCl to H}}_{2}$ is $\text{2 mol HCl"/("1 mol H"_2)}$

$\text{Moles of HCl" = 50 640 color(red)(cancel(color(black)("mol H"_2))) × "2 mol HCl"/(1 color(red)(cancel(color(black)("mol H"_2)))) = "101 280 mol HCl}$

(d) Calculate the volume of $\text{HCl}$

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

$P V = n R T$

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 ${\text{2370 m}}^{3}$ of $\text{HCl}$.