Question

2 NH3 (g) + 3 Cl2(g) = 1 N2(g) + 6 HCl (g)How many liters of ammonia gas at 244 torr and 35 C must be used to produce 235 g of HCl gas?

Answer 1

The volume of ammonia gas is 169.3L

Step-by-step explanation

Given that

The pressure of the gas is 244 torr

The temperature of the gas is 35 degrees Celcius

The mass of HCl is 235g

Follow the steps below to find the volume of the ammonia gas.

Step 1; Write the balanced equation of the reaction

`\text{ 2NH}_(3(g))\text{ + 3Cl}_(2(g))\text{ }\rightarrow\text{ N}_(2(g))\text{ + 6HCl}_((g))`

In the above reaction, 2 moles Ammonia react with 3 moles Cl2 to give 1 mole N2 and 6 moles HCl

Step 2; Find the number of moles of HCl using the below formula

`\text{ mole }=\text{ }\frac{\text{ mass}}{\text{ molar mass}}`

Recall, that the molar mass of HCl is 36.458 g/mol

`\begin{gathered} \text{ mole }=\text{ }(235)/(36.458) \\ \text{ mole = 6.45 moles} \end{gathered}`

Step 3; Find the mole of NH3 using stoichiometry ratio

Recall, 2 moles NH3 give 6 moles HCl

Let x represents the number of moles of NH3

`\begin{gathered} \text{ 2 mole NH}_3\text{ }\rightarrow\text{ 6 mole HCl} \\ \text{ x mole NH}_3\text{ }\rightarrow\text{ 6.45 mole HCl} \\ \text{ cross multiply} \\ \text{ 2 mole NH}_3\text{ }*\text{ 6.45 mole HCl }=\text{ x mole NH}_3*\text{ 6 mole HCl} \\ \text{ Isolate x} \\ \text{ x = }\frac{\text{ 2 mole NH}_3*6.45mole\cancel{HCl}}{6mole\cancel{HCl}} \\ \\ \text{ x = }\frac{2\text{ }*\text{ 6.45}}{6} \\ \text{ x = }(12.9)/(6) \\ \text{ x = 2.15 moles} \end{gathered}`

The number of moles of NH3 is 2.15 moles

Step 4; Find the volume of NH3 using the ideal gas equation

`\text{ PV = nRT}`

Recall that, 35 degrees Celcius = 308.15K

`\begin{gathered} \text{ R = 62.363 L. torr. mol}^(-1).\text{ K}^(-1) \\ \\ \text{ 244 }*\text{ V }=\text{ 2.15 }*\text{ 62.363}*\text{ 308.15} \\ \text{ 244V = 41,316.89} \\ \text{ Divide both sides by 244} \\ \frac{\cancel{244}V}{\cancel{244}}\text{ = }(41316.89)/(244) \\ \text{ V = 169.3 L} \end{gathered}`

Therefore, the volume of ammonia gas is 169.3L