At a certain temperature the rate of this reaction is first order in NH, with a rate constant of 1.22 s : 2NH; (g) → N, (3) + 3H, (2) Suppose a vessel contains NH, at a concentration of 0.450M. Calculate the concentration of NH, in the vessel 0.860 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. ?
At a certain temperature the rate of this reaction is first order in NH, with a rate constant of 1.22 s : 2NH; (g) → N, (3) + 3H, (2) Suppose a vessel contains NH, at a concentration of 0.450M. Calculate the concentration of NH, in the vessel 0.860 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. ?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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![### Reaction Rate and Concentration Calculation
At a certain temperature, the rate of this reaction is first order in \( \text{NH}_3 \) with a rate constant of \( 1.22 \ s^{-1} \):
\[
2\text{NH}_3 \ (g) \rightarrow \text{N}_2 \ (g) + 3\text{H}_2 \ (g)
\]
Suppose a vessel contains \( \text{NH}_3 \) at a concentration of \( 0.450 \ M \). Calculate the concentration of \( \text{NH}_3 \) in the vessel \( 0.860 \) seconds later. You may assume no other reaction is important.
Round your answer to 2 significant digits.
____
\(\boxed{\phantom{0}M}\) \[\checkmark_{x10}\]
**Explanation:**
1. **Identify the Reaction Order and Rate Constant:**
- The reaction is first order in \( \text{NH}_3 \) (ammonia).
- The rate constant \( k \) is \( 1.22 \ s^{-1} \).
2. **Initial Concentration:**
- Initial concentration of \( \text{NH}_3 \) is \( [\text{NH}_3]_0 = 0.450 \ M \).
3. **Use the First Order Reaction Formula:**
- The formula for first-order reactions is:
\[
[\text{NH}_3] = [\text{NH}_3]_0 e^{-kt}
\]
4. **Substitute the Given Values:**
- Time \( t \) is \( 0.860 \) seconds.
- Substitute into the formula:
\[
[\text{NH}_3] = 0.450 \ M \times e^{-1.22 \times 0.860}
\]
5. **Calculate:**
- Calculate the exponent:
\[
-1.22 \times 0.860 \approx -1.0492
\]
- Calculate \( e^{-1.0492} \):
\[
e^{-1.0492} \approx 0.350
\]
- Final concentration:
\[
[\text{NH}_3] \approx 0.450 \ M](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F219723a0-65f7-41ee-870e-9a28c61ab761%2F5da45b9b-7e9f-4bc3-848b-37ee986cfa7d%2Fgqolbet_processed.png&w=3840&q=75)
Transcribed Image Text:### Reaction Rate and Concentration Calculation
At a certain temperature, the rate of this reaction is first order in \( \text{NH}_3 \) with a rate constant of \( 1.22 \ s^{-1} \):
\[
2\text{NH}_3 \ (g) \rightarrow \text{N}_2 \ (g) + 3\text{H}_2 \ (g)
\]
Suppose a vessel contains \( \text{NH}_3 \) at a concentration of \( 0.450 \ M \). Calculate the concentration of \( \text{NH}_3 \) in the vessel \( 0.860 \) seconds later. You may assume no other reaction is important.
Round your answer to 2 significant digits.
____
\(\boxed{\phantom{0}M}\) \[\checkmark_{x10}\]
**Explanation:**
1. **Identify the Reaction Order and Rate Constant:**
- The reaction is first order in \( \text{NH}_3 \) (ammonia).
- The rate constant \( k \) is \( 1.22 \ s^{-1} \).
2. **Initial Concentration:**
- Initial concentration of \( \text{NH}_3 \) is \( [\text{NH}_3]_0 = 0.450 \ M \).
3. **Use the First Order Reaction Formula:**
- The formula for first-order reactions is:
\[
[\text{NH}_3] = [\text{NH}_3]_0 e^{-kt}
\]
4. **Substitute the Given Values:**
- Time \( t \) is \( 0.860 \) seconds.
- Substitute into the formula:
\[
[\text{NH}_3] = 0.450 \ M \times e^{-1.22 \times 0.860}
\]
5. **Calculate:**
- Calculate the exponent:
\[
-1.22 \times 0.860 \approx -1.0492
\]
- Calculate \( e^{-1.0492} \):
\[
e^{-1.0492} \approx 0.350
\]
- Final concentration:
\[
[\text{NH}_3] \approx 0.450 \ M
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