Use this graph to answer the following questions: What is the half life of the reaction? 1/2 = s %3! Round your answer to 2 significant digits. Suppose the rate of the reaction is known to be first order in NH3. Calculate the value of the rate constant k. k = 0 Round your answer to 2 significant digits. Also be sure you include the correct unit symbol. Predict the concentration of NH3 in the engineer's reaction vessel after 0.180 seconds have passed. Assume no other reaction is important, and continue to assume the rate is first order in NH3. [NH,] = 0M %3! Round your answer to 2 significant digits.

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### Analyze Reaction Rates Using a Graph

### Questions and Answers Based on the Graph:

1. **Determine the Half-Life of the Reaction:**
   - **Question:** What is the half-life of the reaction? 
     - **Instructions:** Round your answer to 2 significant digits.
   - **Answer:** \( t_{1/2} = \square \) s

2. **Calculate the Rate Constant (k) for First-Order Reaction in NH₃:**
   - **Question:** Suppose the rate of the reaction is known to be first order in NH₃. Calculate the value of the rate constant \( k \).
     - **Instructions:** Round your answer to 2 significant digits and include the correct unit symbol.
   - **Answer:** \( k = \square \) 

3. **Predict the Concentration of NH₃ Over Time:**
   - **Question:** Predict the concentration of NH₃ in the engineer's reaction vessel after 0.180 seconds have passed. Assume no other reaction is important, and continue to assume the rate is first order in NH₃.
     - **Instructions:** Round your answer to 2 significant digits.
   - **Answer:** \[ NH_{3}] = \square \) M

### Graph and Diagram Explanation:

- **Graph Characteristics:** The graph appears to provide data relevant to the reaction kinetics of \( NH₃ \). Although the image provided does not display the actual graph, typically such graphs will show the concentration of \( NH₃ \) as a function of time, from which you can derive the half-life, calculate the rate constant for a first-order reaction, and predict future concentrations using the relevant formulas.
  
- **Legend and Units:** Ensure to note the x-axis (time in seconds t) and y-axis (concentration in molarity M). This helps in understanding the units for your calculations like the rate constant \( k \) in s⁻¹.

### Note to Educators:
When working with students on these questions, guide them through the process of deriving calculations from the graph. Emphasize the significance of understanding the graphical data to determine key kinetic parameters and predict future behavior of the reaction. This exercise enhances their comprehension in theoretical and practical aspects of chemical kinetics.
Transcribed Image Text:### Analyze Reaction Rates Using a Graph ### Questions and Answers Based on the Graph: 1. **Determine the Half-Life of the Reaction:** - **Question:** What is the half-life of the reaction? - **Instructions:** Round your answer to 2 significant digits. - **Answer:** \( t_{1/2} = \square \) s 2. **Calculate the Rate Constant (k) for First-Order Reaction in NH₃:** - **Question:** Suppose the rate of the reaction is known to be first order in NH₃. Calculate the value of the rate constant \( k \). - **Instructions:** Round your answer to 2 significant digits and include the correct unit symbol. - **Answer:** \( k = \square \) 3. **Predict the Concentration of NH₃ Over Time:** - **Question:** Predict the concentration of NH₃ in the engineer's reaction vessel after 0.180 seconds have passed. Assume no other reaction is important, and continue to assume the rate is first order in NH₃. - **Instructions:** Round your answer to 2 significant digits. - **Answer:** \[ NH_{3}] = \square \) M ### Graph and Diagram Explanation: - **Graph Characteristics:** The graph appears to provide data relevant to the reaction kinetics of \( NH₃ \). Although the image provided does not display the actual graph, typically such graphs will show the concentration of \( NH₃ \) as a function of time, from which you can derive the half-life, calculate the rate constant for a first-order reaction, and predict future concentrations using the relevant formulas. - **Legend and Units:** Ensure to note the x-axis (time in seconds t) and y-axis (concentration in molarity M). This helps in understanding the units for your calculations like the rate constant \( k \) in s⁻¹. ### Note to Educators: When working with students on these questions, guide them through the process of deriving calculations from the graph. Emphasize the significance of understanding the graphical data to determine key kinetic parameters and predict future behavior of the reaction. This exercise enhances their comprehension in theoretical and practical aspects of chemical kinetics.
### Reaction Rate Study of Ammonia Decomposition

A chemical engineer is investigating the rate of the following reaction:

\[ 2NH_3(g) \rightarrow N_2(g) + 3H_2(g) \]

To study the reaction, he fills a reaction vessel with ammonia (\( NH_3 \)) and monitors its concentration over time. Below is the graph that illustrates the concentration of \( NH_3 \) (\( [NH_3] \)) as the reaction progresses:

#### Graph Description

The y-axis represents the concentration of \( NH_3 \) in molarity (\( M \)).
The x-axis represents time (\( t \)) in seconds (\( s \)).

- The graph shows a decreasing curve indicating the reduction in \( NH_3 \) concentration over time.
- Initially, at \( t = 0 \), the concentration of \( NH_3 \) is at its maximum, starting from 1 M.
- As time progresses, the concentration of \( NH_3 \) decreases non-linearly, suggesting a rapid initial reaction rate that slows down as the concentration of \( NH_3 \) approaches zero.
- By \( t \approx 0.10 \, s \), the concentration of \( NH_3 \) is nearly zero, indicating the reaction has nearly reached completion.

This graph can be utilized to further analyze the kinetics of the reaction, determine the reaction order, and calculate the rate constant.
Transcribed Image Text:### Reaction Rate Study of Ammonia Decomposition A chemical engineer is investigating the rate of the following reaction: \[ 2NH_3(g) \rightarrow N_2(g) + 3H_2(g) \] To study the reaction, he fills a reaction vessel with ammonia (\( NH_3 \)) and monitors its concentration over time. Below is the graph that illustrates the concentration of \( NH_3 \) (\( [NH_3] \)) as the reaction progresses: #### Graph Description The y-axis represents the concentration of \( NH_3 \) in molarity (\( M \)). The x-axis represents time (\( t \)) in seconds (\( s \)). - The graph shows a decreasing curve indicating the reduction in \( NH_3 \) concentration over time. - Initially, at \( t = 0 \), the concentration of \( NH_3 \) is at its maximum, starting from 1 M. - As time progresses, the concentration of \( NH_3 \) decreases non-linearly, suggesting a rapid initial reaction rate that slows down as the concentration of \( NH_3 \) approaches zero. - By \( t \approx 0.10 \, s \), the concentration of \( NH_3 \) is nearly zero, indicating the reaction has nearly reached completion. This graph can be utilized to further analyze the kinetics of the reaction, determine the reaction order, and calculate the rate constant.
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