Consider this reaction: NH,OH (аq) - NH, (aq)+H2O (aq) At a certain temperature it obeys this rate law. rate = (0.00107 s ')[NH,OH] Suppose a vessel contains NH OH at a concentration of 0.650M. Calculate the concentration of NH,OH in the vessel 860. seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. OM

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### Chemical Reaction and Rate Law

**Consider this reaction:**

\[ \text{NH}_4\text{OH} (\text{aq}) \rightarrow \text{NH}_3 (\text{aq}) + \text{H}_2\text{O} (\text{aq}) \]

At a certain temperature, it obeys this rate law:

\[ \text{rate} = (0.00107 \ \text{s}^{-1}) [\text{NH}_4\text{OH}] \]

**Problem Statement:**

Suppose a vessel contains \(\text{NH}_4\text{OH}\) at a concentration of \(0.650 \ \text{M}\). Calculate the concentration of \(\text{NH}_4\text{OH}\) in the vessel 860 seconds later. You may assume no other reaction is important.

Round your answer to 2 significant digits.

**Graph or Diagram Explanation:**

In the given image, there is a blank box followed by the unit 'M' (molarity), indicating that this is where the calculated concentration should be entered. Additionally, there are options indicated by various icons, typically used for checking, resetting, or getting help.

**Calculations:**

This reaction follows a first-order kinetics model, and the concentration of \(\text{NH}_4\text{OH}\) can be calculated using the formula for first-order reactions:
\[ [\text{NH}_4\text{OH}]_t = [\text{NH}_4\text{OH}]_0 e^{-kt} \]

Where:
- \( [\text{NH}_4\text{OH}]_t \) is the concentration at time \( t \).
- \( [\text{NH}_4\text{OH}]_0 \) is the initial concentration.
- \( k \) is the rate constant (0.00107 \(\text{s}^{-1}\)).
- \( t \) is the time elapsed (860 seconds).

Substituting the given values:

\[ [\text{NH}_4\text{OH}]_{860} = 0.650 \ \text{M} \times e^{-(0.00107 \ \text{s}^{-1})(860 \ \text{s})} \]

\[ [\text{NH}_4\text{OH}]_{860} = 0.650 \ \
Transcribed Image Text:### Chemical Reaction and Rate Law **Consider this reaction:** \[ \text{NH}_4\text{OH} (\text{aq}) \rightarrow \text{NH}_3 (\text{aq}) + \text{H}_2\text{O} (\text{aq}) \] At a certain temperature, it obeys this rate law: \[ \text{rate} = (0.00107 \ \text{s}^{-1}) [\text{NH}_4\text{OH}] \] **Problem Statement:** Suppose a vessel contains \(\text{NH}_4\text{OH}\) at a concentration of \(0.650 \ \text{M}\). Calculate the concentration of \(\text{NH}_4\text{OH}\) in the vessel 860 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. **Graph or Diagram Explanation:** In the given image, there is a blank box followed by the unit 'M' (molarity), indicating that this is where the calculated concentration should be entered. Additionally, there are options indicated by various icons, typically used for checking, resetting, or getting help. **Calculations:** This reaction follows a first-order kinetics model, and the concentration of \(\text{NH}_4\text{OH}\) can be calculated using the formula for first-order reactions: \[ [\text{NH}_4\text{OH}]_t = [\text{NH}_4\text{OH}]_0 e^{-kt} \] Where: - \( [\text{NH}_4\text{OH}]_t \) is the concentration at time \( t \). - \( [\text{NH}_4\text{OH}]_0 \) is the initial concentration. - \( k \) is the rate constant (0.00107 \(\text{s}^{-1}\)). - \( t \) is the time elapsed (860 seconds). Substituting the given values: \[ [\text{NH}_4\text{OH}]_{860} = 0.650 \ \text{M} \times e^{-(0.00107 \ \text{s}^{-1})(860 \ \text{s})} \] \[ [\text{NH}_4\text{OH}]_{860} = 0.650 \ \
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