Nitrogen gas \(\left(\mathrm{N}_{2}\right)\) reacts with hydrogen gas \(\left(\mathrm{H}_{2}\right)\) to form ammonia gas \(\left(\mathrm{NH}_{3}\right) .\) You have nitrogen and hydrogen gases in a \(15.0\)-\(\mathrm{L}\) container fitted with a movable piston (the piston allows the container volume to change so as to keep the pressure constant inside the container). Initially the partial pressure of each reactant gas is \(1.00\) atm. Assume the temperature is constant and that the reaction goes to completion. a. Calculate the partial pressure of ammonia in the container after the reaction has reached completion. b. Calculate the volume of the container after the reaction has reached completion.

Step by step solution

01

Write Down the Balanced Reaction

Nitrogen gas reacts with hydrogen gas to form ammonia gas according to the following balanced chemical equation: \( N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) \) #Step II: Calculate Moles of Reactant Gases#

02

Calculate Moles of Reactant Gases

We know the initial partial pressures of the nitrogen and hydrogen gases. To find the moles, 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 (\(0.0821 \ L \ atm \ K^{−1} mol^{−1}\)) \(T\) is Temperature (in Kelvin) Solve for the moles (\(n\)) of \(N_2\) and \(H_2\): \( n_{N_2} = \frac{P_{N_2}V}{RT}\) \( n_{H_2} = \frac{P_{H_2}V}{RT}\) Since both nitrogen and hydrogen gases have the same pressure (\(P = 1.00 \ atm\)) and volume (\(V = 15.0 \ L\)), their moles will be the same as well. #Step III: Determine Mole Ratios of Reaction Components#

03

Determine Mole Ratios of Reaction Components

Use the balanced chemical equation to determine the mole ratios of the reaction components: For nitrogen gas (\(N_2\)), the mole ratio is 1:1, For hydrogen gas (\(H_2\)), the mole ratio is 3:1, For ammonia gas (\(NH_3\)), the mole ratio is 2:1. #Step IV: Calculate Moles and Partial Pressure of Ammonia Gas (NH3)#

04

Calculate Moles and Partial Pressure of Ammonia Gas

From stoichiometry, we could conclude that upon complete reaction, all the nitrogen and three times the amount of hydrogen would be used to form 2 times the amount of ammonia. Calculate moles of ammonia gas: \(n_{NH3} = 2 \times n_{N2}\) Use the moles of ammonia gas to find its partial pressure: \(P_{NH3} = \frac{n_{NH3}RT}{V}\) #Step V: Calculate the Final Volume of the Container#

05

Calculate the Final Volume of the Container

Since the pressure remains constant inside the container, the final starting and ending pressures in the container (partial pressures of all gases) are the same. Total initial pressure: \(P_{Initial} = P_{N_2} + P_{H_2}\) Total final pressure: \(P_{Final} = P_{NH_3}\) Since the pressure inside the container is constant, we have: \(P_{Initial} = P_{Final}\) Solve for the final volume of the container: \(V_{Final} = \frac{P_{Initial}}{P_{Final}} \times V_{Initial}\) Now you can plug in the values obtained in the previous steps and calculate the answers for a) partial pressure of ammonia gas and b) the final volume of the container.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!