A chemistry graduate student is studying the rate of this reaction: H₂CO3 (aq)→ H₂O (aq) + CO₂ (aq) She fills a reaction vessel with H₂CO3 and measures its concentration as the reaction proceeds: time (seconds) 0 1.0 2.0 3.0 4.0 [H,CO,] 0.800M 0.144M 0.0794M 0.0547 M 0.0418M Use this data to answer the following questions. Write the rate law for this reaction. Calculate the value of the rate constant k. Round your answer to 2 significant digits. Also be sure your answer has the correct unit symbol. rate = k k = 0 x10 ロ・ロ X 2 4

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**Title: Understanding Reaction Rates – A Case Study**

**Overview:**
A chemistry graduate student is studying the rate of the reaction:

\[ \text{H}_2\text{CO}_3 \,(\text{aq}) \rightarrow \text{H}_2\text{O} \,(\text{aq}) + \text{CO}_2 \,(\text{aq}) \]

She fills a reaction vessel with \(\text{H}_2\text{CO}_3\) and measures its concentration as the reaction proceeds.

**Data Table:**

| Time (seconds) | \([\text{H}_2\text{CO}_3]\) |
|----------------|----------------------|
| 0              | 0.800 M              |
| 1.0            | 0.144 M              |
| 2.0            | 0.0794 M             |
| 3.0            | 0.0547 M             |
| 4.0            | 0.0418 M             |

**Instructions:**
Use this data to answer the following questions.

1. **Write the rate law for this reaction:**

   \[
   \text{rate} = k [\text{H}_2\text{CO}_3]
   \]

2. **Calculate the value of the rate constant \(k\):**

   Round your answer to 2 significant digits. Also, ensure your answer has the correct unit symbol.

   \[
   k = \, [\text{Enter your answer here}]
   \]

**Graph Explanation:**

The graph provided illustrates changes in \([\text{H}_2\text{CO}_3]\) over time, with concentration on the y-axis and time on the x-axis. The data points plot the measured concentrations at each time interval. Analysis of these points helps determine the rate of reaction and calculate the rate constant. 

**Note:**
Ensure calculations reflect changes in concentration over time to properly derive \(k\).
Transcribed Image Text:**Title: Understanding Reaction Rates – A Case Study** **Overview:** A chemistry graduate student is studying the rate of the reaction: \[ \text{H}_2\text{CO}_3 \,(\text{aq}) \rightarrow \text{H}_2\text{O} \,(\text{aq}) + \text{CO}_2 \,(\text{aq}) \] She fills a reaction vessel with \(\text{H}_2\text{CO}_3\) and measures its concentration as the reaction proceeds. **Data Table:** | Time (seconds) | \([\text{H}_2\text{CO}_3]\) | |----------------|----------------------| | 0 | 0.800 M | | 1.0 | 0.144 M | | 2.0 | 0.0794 M | | 3.0 | 0.0547 M | | 4.0 | 0.0418 M | **Instructions:** Use this data to answer the following questions. 1. **Write the rate law for this reaction:** \[ \text{rate} = k [\text{H}_2\text{CO}_3] \] 2. **Calculate the value of the rate constant \(k\):** Round your answer to 2 significant digits. Also, ensure your answer has the correct unit symbol. \[ k = \, [\text{Enter your answer here}] \] **Graph Explanation:** The graph provided illustrates changes in \([\text{H}_2\text{CO}_3]\) over time, with concentration on the y-axis and time on the x-axis. The data points plot the measured concentrations at each time interval. Analysis of these points helps determine the rate of reaction and calculate the rate constant. **Note:** Ensure calculations reflect changes in concentration over time to properly derive \(k\).
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