https://file.aiquickdraw.com/mathbot/file/1728849584295l3wejpxb.jpg

In this image, we are asked to predict the equilibrium pressure of ammonia (\( \text{NH}_3 \)) using the provided equilibrium data and tools.

We have the following chemical equilibrium:

\[
\text{N}_2(g) + 3 \text{H}_2(g) \rightleftharpoons 2 \text{NH}_3(g)
\]
with the equilibrium constant \( K_p = 3.1 \times 10^{-7} \).

Initial conditions are:
- \( \text{N}_2 \) partial pressure = 1.1 atm
- \( \text{H}_2 \) partial pressure = 4.1 atm.

### To solve:
1. **Set up the ICE table** (Initial, Change, Equilibrium) for the reaction:
   \[
   \begin{array}{c|c|c|c}
   \text{Species} & \text{N}_2 & \text{H}_2 & \text{NH}_3 \\
   \hline
   \text{Initial (atm)} & 1.1 & 4.1 & 0 \\
   \text{Change (atm)} & -x & -3x & +2x \\
   \text{Equilibrium (atm)} & 1.1 - x & 4.1 - 3x & 2x \\
   \end{array}
   \]
   
2. **Expression for \( K_p \)**:
   \[
   K_p = \frac{(P_{\text{NH}_3})^2}{(P_{\text{N}_2})(P_{\text{H}_2})^3} = 3.1 \times 10^{-7}
   \]
   Substituting equilibrium pressures:
   \[
   K_p = \frac{(2x)^2}{(1.1 - x)(4.1 - 3x)^3} = 3.1 \times 10^{-7}
   \]

3. **Small \( x \) approximation**: Since \( K_p \) is very small, we assume that \( x \) is small, so \( 1.1 - x \approx 1.1 \) and \( 4.1 - 3x \approx 4.1 \). Simplifying:
   \[
   K_p = \frac{(2x)^2}{(1.1)(4.1)^3}
   \]
   Solving for \( x \):
   \[
   3.1 \times 10^{-7} = \frac{4x^2}{1.1 \times 69.921}
   \]
   \[
   3.1 \times 10^{-7} = \frac{4x^2}{76.9131}
   \]
   \[
   x^2 = \frac{3.1 \times 10^{-7} \times 76.9131}{4}
   \]
   \[
   x^2 \approx 5.96 \times 10^{-6}
   \]
   \[
   x \approx 0.00244
   \]

4. **Equilibrium pressure of \( \text{NH}_3 \)**:
   \[
   P_{\text{NH}_3} = 2x = 2 \times 0.00244 = 0.00488 \, \text{atm}
   \]
   Rounding to 1 significant digit: \( P_{\text{NH}_3} \approx 0.005 \, \text{atm} \).

Would you like more details or have any questions?

### Further questions:
1. How does the ICE table help in equilibrium calculations?
2. What is the purpose of the small \( x \) approximation?
3. When should the small \( x \) approximation be used?
4. Can the approximation be used if \( K_p \) is larger?
5. How do you determine when the small \( x \) approximation is valid?

### Tip:
Always verify if your small \( x \) approximation is valid by checking that the calculated value of \( x \) is much smaller than the initial concentrations or pressures.

Can you predict the equilibrium pressure of NH₃ using only the tools available to you within ALEKS? The reaction involves N₂(g), H₂(g), and NH₃(g) with a given equilibrium constant, Kp = 3.1 x 10⁻⁷, and initial conditions: 1.1 atm N₂ and 4.1 atm H₂.

Learn how to calculate the equilibrium pressure of NH₃ for the reaction N₂(g) + 3 H₂(g) ⇌ 2 NH₃(g), given an equilibrium constant Kp = 3.1 x 10⁻⁷. This problem covers key concepts in chemical equilibrium and the use of the small x approximation, with initial conditions of 1.1 atm N₂ and 4.1 atm H₂.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation