A + B → C [A](M)[B](M)Initial Rate (M/h) 0.200 0.221 122 0.893 0.221 230 0.200 0.409 858 Find the order with respect to A. Round to the nearest whole number.

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### Reaction Rate Analysis

**Reaction: A + B → C**

Below is the data table summarizing the concentrations of reactants A and B, and the initial rate of product formation, C. The rate of C formed is given in Molarity per hour (M/h).

| [A] (M) | [B] (M) | Initial Rate (M/h) |
|---------|---------|--------------------|
| 0.200   | 0.221   | 122                |
| 0.893   | 0.221   | 230                |
| 0.200   | 0.409   | 858                |

**Objective:**
Determine the order of reaction with respect to reactant A. Round to the nearest whole number.

**Analysis:**
To determine the order of the reaction with respect to A, you should:
1. Compare the change in the initial rate when the concentration of A is altered, keeping concentration of B constant.
2. Utilize the rate law expression \( \text{Rate} = k [A]^m [B]^n \), where:
   - \( k \) is the rate constant
   - \( m \) and \( n \) are the orders of the reaction with respect to A and B, respectively

**Steps:**
1. From the table, identify experiments where the concentration of B is constant and only the concentration of A changes.
2. Calculate the ratio of rates and the ratio of the concentrations of A for these experiments and determine the reaction order.

For example, between the first and second experiments:
\[ \frac{230}{122} \approx 1.89 \]
\[ \frac{0.893}{0.200} \approx 4.465 \]

Using the rate law expression:
\[ \left( \frac{0.893}{0.200} \right)^m = \frac{230}{122}  \]
\[ (4.465)^m \approx 1.89 \]
\[ m \approx \log_{4.465}(1.89) \]
\[ m \approx 0.5 \]

Round 0.5 to the nearest whole number to get the order of the reaction with respect to A.

**Conclusion:**
The order of the reaction with respect to A is approximately 0 (rounded to the nearest whole number).

Please note this is an approximation and for precise calculations further
Transcribed Image Text:### Reaction Rate Analysis **Reaction: A + B → C** Below is the data table summarizing the concentrations of reactants A and B, and the initial rate of product formation, C. The rate of C formed is given in Molarity per hour (M/h). | [A] (M) | [B] (M) | Initial Rate (M/h) | |---------|---------|--------------------| | 0.200 | 0.221 | 122 | | 0.893 | 0.221 | 230 | | 0.200 | 0.409 | 858 | **Objective:** Determine the order of reaction with respect to reactant A. Round to the nearest whole number. **Analysis:** To determine the order of the reaction with respect to A, you should: 1. Compare the change in the initial rate when the concentration of A is altered, keeping concentration of B constant. 2. Utilize the rate law expression \( \text{Rate} = k [A]^m [B]^n \), where: - \( k \) is the rate constant - \( m \) and \( n \) are the orders of the reaction with respect to A and B, respectively **Steps:** 1. From the table, identify experiments where the concentration of B is constant and only the concentration of A changes. 2. Calculate the ratio of rates and the ratio of the concentrations of A for these experiments and determine the reaction order. For example, between the first and second experiments: \[ \frac{230}{122} \approx 1.89 \] \[ \frac{0.893}{0.200} \approx 4.465 \] Using the rate law expression: \[ \left( \frac{0.893}{0.200} \right)^m = \frac{230}{122} \] \[ (4.465)^m \approx 1.89 \] \[ m \approx \log_{4.465}(1.89) \] \[ m \approx 0.5 \] Round 0.5 to the nearest whole number to get the order of the reaction with respect to A. **Conclusion:** The order of the reaction with respect to A is approximately 0 (rounded to the nearest whole number). Please note this is an approximation and for precise calculations further
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