Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

For the reaction

[tex]\[ 3H_2(g) + N_2(g) \rightleftharpoons 2NH_3(g) \][/tex]

at [tex]\( 225^{\circ}C \)[/tex], the equilibrium constant is [tex]\( 1.7 \times 10^2 \)[/tex]. The equilibrium mixture contains [tex]\( 0.13 \, M \, H_2 \)[/tex] and [tex]\( 0.025 \, M \, N_2 \)[/tex]. What is the molar concentration of [tex]\( NH_3 \)[/tex]?

Express your answer to two significant figures and include the appropriate units.

[tex]\[ \left[ NH_3 \right] = \, \boxed{\hspace{2cm}} \, \text{Units} \][/tex]

Sagot :

GinnyAnswer
Sure! Let's solve this step by step:

### 1. Write down the equilibrium expression:

For the reaction:
[tex]\[ 3 H_2(g) + N_2(g) \rightleftharpoons 2 NH_3(g) \][/tex]

The equilibrium constant expression ([tex]\( K_{eq} \)[/tex]) is given by:
[tex]\[ K_{eq} = \frac{[NH_3]^2}{[H_2]^3 \cdot [N_2]} \][/tex]

### 2. Insert the given equilibrium values:

- [tex]\( K_{eq} = 1.7 \times 10^2 \)[/tex]
- [tex]\( [H_2] = 0.13 \)[/tex] M
- [tex]\( [N_2] = 0.025 \)[/tex] M

We need to find the concentration of [tex]\( NH_3 \)[/tex], denoted as [tex]\( [NH_3] \)[/tex].

### 3. Calculate the concentration of [tex]\( [H_2]^3 \)[/tex]:

[tex]\[ [H_2]^3 = (0.13)^3 = 0.002197 \][/tex]

### 4. Use the equilibrium constant to solve for [tex]\( [NH_3]^2 \)[/tex]:

[tex]\[ K_{eq} = \frac{[NH_3]^2}{[H_2]^3 \cdot [N_2]} \][/tex]

Rearranging for [tex]\( [NH_3]^2 \)[/tex]:

[tex]\[ [NH_3]^2 = K_{eq} \cdot [H_2]^3 \cdot [N_2] \][/tex]

[tex]\[ [NH_3]^2 = 1.7 \times 10^2 \cdot 0.002197 \cdot 0.025 \][/tex]
[tex]\[ [NH_3]^2 = 0.00933725 \][/tex]

### 5. Solve for [tex]\( [NH_3] \)[/tex]:

[tex]\[ [NH_3] = \sqrt{0.00933725} \][/tex]
[tex]\[ [NH_3] \approx 0.09663 \][/tex]

### 6. Expressing the concentration to two significant figures:

[tex]\[ [NH_3] = 0.097 \, \text{M} \][/tex]

### Final Answer:

[tex]\[ \left[ NH_3 \right] = 0.097 \, \text{M} \][/tex]

Therefore, the molar concentration of [tex]\( NH_3 \)[/tex] at equilibrium is [tex]\( 0.097 \)[/tex] M.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.