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?

Question

Luna Chen · Accepted Answer

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

Given: Volume of #"H"_2# at STP; #P# and #T# of #"HCl"#; chemical equation (understood) Find: Volume of #"HCl"# Method: Converting moles of one substance to moles of another is the main task in any stoichiometry problem. (A) The reaction's balanced chemical equation is where we begin. (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 entire approach 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"# Resolution (a) The equation in balance 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"#.

Cooper Adams · Answer

undefined To solve this problem, we can use the ideal gas law, $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is temperature.

First, we need to find the number of moles of hydrogen gas at STP using the equation:

$$
n = \frac{PV}{RT}
$$

Then, we use the balanced chemical equation for the reaction between hydrogen gas and chlorine gas to determine the ratio of moles of hydrogen gas to moles of hydrogen chloride gas produced.

Finally, we use this ratio to find the volume of hydrogen chloride gas produced at the given conditions.

Given:
- $P_{\text{H}_2} = 101.3 \text{ kPa}$ (STP)
- $V_{\text{H}_2} = 1150 \text{ m}^3$
- $P_{\text{HCl}} = 105 \text{ kPa}$
- $T_{\text{HCl}} = 296 \text{ K}$
- $R = 8.314 \text{ J/mol}\cdot\text{K}$ (ideal gas constant)

First, find the number of moles of hydrogen gas at STP:

$$
n_{\text{H}_2} = \frac{P_{\text{H}_2} \cdot V_{\text{H}_2}}{R \cdot T_{\text{STP}}}
$$

Substitute the given values:

$$
n_{\text{H}_2} = \frac{101.3 \times 10^3 \times 1150}{8.314 \times 273.15}
$$

Then, determine the ratio of moles of hydrogen chloride gas to moles of hydrogen gas from the balanced chemical equation:

$$ \text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl} $$

The ratio is 2 moles of HCl produced for every 1 mole of H2 consumed.

Now, multiply the number of moles of hydrogen gas by the ratio to find the number of moles of hydrogen chloride gas produced:

$$ n_{\text{HCl}} = 2 \times n_{\text{H}_2} $$

Finally, use the ideal gas law to find the volume of hydrogen chloride gas produced at the given conditions:

$$ V_{\text{HCl}} = \frac{n_{\text{HCl}} \cdot R \cdot T_{\text{HCl}}}{P_{\text{HCl}}} $$

Substitute the values and solve for $V_{\text{HCl}}$.