At a certain temperature this reaction follows second-order kinetics with a rate constant of 0.0159M¹¹; H,CO, (aq) →H,O(aq)+CO,(aq) Suppose a vessel contains H₂CO3 at a concentration of 1.04M. Calculate the concentration of H₂CO3 in the vessel 610. seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. M

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### Second-Order Kinetics Example

At a certain temperature, this reaction follows second-order kinetics with a rate constant of \( 0.0159 \, M^{-1} \cdot s^{-1} \):

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

Suppose a vessel contains \(\text{H}_2\text{CO}_3\) at a concentration of \(1.04 \, M\). Calculate the concentration of \(\text{H}_2\text{CO}_3\) in the vessel 610 seconds later. You may assume no other reaction is important.

Round your answer to 2 significant digits.

### Given Data

1. Initial concentration of \(\text{H}_2\text{CO}_3\) (\( [\text{H}_2\text{CO}_3]_0 \)) = 1.04 M
2. Rate constant (k) = \( 0.0159 \, M^{-1} \cdot s^{-1} \)
3. Time (t) = 610 seconds

### Second-Order Kinetics Formula

For a second-order reaction, the concentration at time \( t \) can be calculated using the formula:

\[ \frac{1}{[\text{A}]_t} = kt + \frac{1}{[\text{A}]_0} \]

Where:
- \([A]_t\) is the concentration at time \( t \)
- \( k \) is the rate constant
- \( [A]_0 \) is the initial concentration
- \( t \) is the time

### Calculation

1. Substitute the given values into the second-order kinetics formula:

\[ \frac{1}{[\text{H}_2\text{CO}_3]_t} = 0.0159 \times 610 + \frac{1}{1.04} \]

2. Perform the calculation:

\[ \frac{1}{[\text{H}_2\text{CO}_3]_t} = 0.0159 \times 610 + 0.9615 \]

\[ \frac{1}{[\text{H}_2\text{CO}_3]_t} = 9.
Transcribed Image Text:### Second-Order Kinetics Example At a certain temperature, this reaction follows second-order kinetics with a rate constant of \( 0.0159 \, M^{-1} \cdot s^{-1} \): \[ \text{H}_2\text{CO}_3 (aq) \rightarrow \text{H}_2\text{O} (aq) + \text{CO}_2 (aq) \] Suppose a vessel contains \(\text{H}_2\text{CO}_3\) at a concentration of \(1.04 \, M\). Calculate the concentration of \(\text{H}_2\text{CO}_3\) in the vessel 610 seconds later. You may assume no other reaction is important. Round your answer to 2 significant digits. ### Given Data 1. Initial concentration of \(\text{H}_2\text{CO}_3\) (\( [\text{H}_2\text{CO}_3]_0 \)) = 1.04 M 2. Rate constant (k) = \( 0.0159 \, M^{-1} \cdot s^{-1} \) 3. Time (t) = 610 seconds ### Second-Order Kinetics Formula For a second-order reaction, the concentration at time \( t \) can be calculated using the formula: \[ \frac{1}{[\text{A}]_t} = kt + \frac{1}{[\text{A}]_0} \] Where: - \([A]_t\) is the concentration at time \( t \) - \( k \) is the rate constant - \( [A]_0 \) is the initial concentration - \( t \) is the time ### Calculation 1. Substitute the given values into the second-order kinetics formula: \[ \frac{1}{[\text{H}_2\text{CO}_3]_t} = 0.0159 \times 610 + \frac{1}{1.04} \] 2. Perform the calculation: \[ \frac{1}{[\text{H}_2\text{CO}_3]_t} = 0.0159 \times 610 + 0.9615 \] \[ \frac{1}{[\text{H}_2\text{CO}_3]_t} = 9.
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