3 4 1 5 6 7 8 At a certain temperature the rate of this reaction is first order in HI with a rate constant of 0.0797 s 2HI (g) → H₂(g) + 1₂ (8) Suppose a vessel contains HI at a concentration of 0.870 M. Calculate the concentration of HI in the vessel 10.0 seconds later. You may assume no other. reaction is important. Round your answer to 2 significant digits. M ? x10 X S

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**Chemical Kinetics Problem**

---

**Problem Statement:**

At a certain temperature, the rate of this reaction is first order in HI with a rate constant of \( 0.0797 \, \text{s}^{-1} \):

\[ 2HI(g) \rightarrow H_2(g) + I_2(g) \]

Suppose a vessel contains HI at a concentration of \( 0.870 \, M \). Calculate the concentration of HI in the vessel 10.0 seconds later. You may assume no other reaction is important.

Round your answer to 2 significant digits.

**Answer Input:**
- Box labeled " \( M \)" for answer input
- Options for exponents (\( \times 10^{x} \)), reset (\( \return \)), and help (\( ? \))

*Interactive Elements and Design:* 

At the top of the screen, there are sequential numbered tabs (1, 3, 4, 5, 6, 7, 8) indicating the progression through a set of problems or sections. The design suggests that the user is currently on problem 1, as it is highlighted.

At the bottom, there is a "Continue" button to proceed after entering the answer.

**Steps to Solve:**

1. **Identify the Rate Law:**
   Since the reaction is first order in HI, the rate law can be written as:
   \[
   \text{Rate} = k [\text{HI}]
   \]
   where \( k = 0.0797 \, \text{s}^{-1} \).

2. **Use the First-Order Integrated Rate Law:**
   The integrated rate law for a first-order reaction is:
   \[
   \ln \left( \frac{[\text{HI}]_t}{[\text{HI}]_0} \right) = -kt
   \]
   Given:
   \[
   [\text{HI}]_0 = 0.870 \, M, \quad t = 10.0 \, \text{s}
   \]

3. **Plug in Values to Solve for \([\text{HI}]_t\):**
   \[
   \ln \left( \frac{[\text{HI}]_t}{0.870} \right) = - (0.0797) (10.0)
   \]
Transcribed Image Text:**Chemical Kinetics Problem** --- **Problem Statement:** At a certain temperature, the rate of this reaction is first order in HI with a rate constant of \( 0.0797 \, \text{s}^{-1} \): \[ 2HI(g) \rightarrow H_2(g) + I_2(g) \] Suppose a vessel contains HI at a concentration of \( 0.870 \, M \). Calculate the concentration of HI in the vessel 10.0 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. **Answer Input:** - Box labeled " \( M \)" for answer input - Options for exponents (\( \times 10^{x} \)), reset (\( \return \)), and help (\( ? \)) *Interactive Elements and Design:* At the top of the screen, there are sequential numbered tabs (1, 3, 4, 5, 6, 7, 8) indicating the progression through a set of problems or sections. The design suggests that the user is currently on problem 1, as it is highlighted. At the bottom, there is a "Continue" button to proceed after entering the answer. **Steps to Solve:** 1. **Identify the Rate Law:** Since the reaction is first order in HI, the rate law can be written as: \[ \text{Rate} = k [\text{HI}] \] where \( k = 0.0797 \, \text{s}^{-1} \). 2. **Use the First-Order Integrated Rate Law:** The integrated rate law for a first-order reaction is: \[ \ln \left( \frac{[\text{HI}]_t}{[\text{HI}]_0} \right) = -kt \] Given: \[ [\text{HI}]_0 = 0.870 \, M, \quad t = 10.0 \, \text{s} \] 3. **Plug in Values to Solve for \([\text{HI}]_t\):** \[ \ln \left( \frac{[\text{HI}]_t}{0.870} \right) = - (0.0797) (10.0) \]
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