The following data are for the decomposition of dinitrogen pentoxide in carbon tetrachloride solution at 30 °C. N₂O5 →→→2 NO₂ + 12 02 [N₂05 ], M 0.200 0.100 5.00×10-² time, min 0 133 266 Hint: It is not necessary to graph these data. (1) The half life observed for this reaction is 133 (2) Based on these data, the rate constant for this reaction is min -¹. min. order 2.50x10-2 399

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### Decomposition of Dinitrogen Pentoxide in Carbon Tetrachloride Solution at 30 °C

**Reaction:**
\[ N_2O_5 \rightarrow 2 NO_2 + \frac{1}{2} O_2 \]

**Experimental Data:**

| \([ N_2O_5 ]\), M | 0.200 | 0.100 | 5.00 × 10⁻² | 2.50 × 10⁻² |
|-------------------|-------|-------|-------------|-------------|
| **time, min**     | 0     | 133   | 266         | 399         |

**Hint: It is not necessary to graph these data.**

**Questions:**

1. The half-life observed for this reaction is \( \boxed{133} \) min.
2. Based on these data, the rate constant for this \( \boxed{\text{}} \) order reaction is \( \boxed{\text{}} \) min⁻¹.

### Explanation of the Data Table

The table presents the concentration of \( N_2O_5 \) (in molarity, M) at various time intervals (in minutes, min). The concentrations decrease over time as the decomposition reaction proceeds, reflecting the consumption of \( N_2O_5 \):

- At time \( t = 0 \) minutes, the concentration of \( N_2O_5 \) is 0.200 M.
- At time \( t = 133 \) minutes, the concentration decreases to 0.100 M, indicating the half-life of the reaction.
- At time \( t = 266 \) minutes, the concentration further decreases to 5.00 × 10⁻² M.
- At time \( t = 399 \) minutes, the concentration decreases to 2.50 × 10⁻² M.

This data illustrates the progress of the reaction over time.
Transcribed Image Text:### Decomposition of Dinitrogen Pentoxide in Carbon Tetrachloride Solution at 30 °C **Reaction:** \[ N_2O_5 \rightarrow 2 NO_2 + \frac{1}{2} O_2 \] **Experimental Data:** | \([ N_2O_5 ]\), M | 0.200 | 0.100 | 5.00 × 10⁻² | 2.50 × 10⁻² | |-------------------|-------|-------|-------------|-------------| | **time, min** | 0 | 133 | 266 | 399 | **Hint: It is not necessary to graph these data.** **Questions:** 1. The half-life observed for this reaction is \( \boxed{133} \) min. 2. Based on these data, the rate constant for this \( \boxed{\text{}} \) order reaction is \( \boxed{\text{}} \) min⁻¹. ### Explanation of the Data Table The table presents the concentration of \( N_2O_5 \) (in molarity, M) at various time intervals (in minutes, min). The concentrations decrease over time as the decomposition reaction proceeds, reflecting the consumption of \( N_2O_5 \): - At time \( t = 0 \) minutes, the concentration of \( N_2O_5 \) is 0.200 M. - At time \( t = 133 \) minutes, the concentration decreases to 0.100 M, indicating the half-life of the reaction. - At time \( t = 266 \) minutes, the concentration further decreases to 5.00 × 10⁻² M. - At time \( t = 399 \) minutes, the concentration decreases to 2.50 × 10⁻² M. This data illustrates the progress of the reaction over time.
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