Which of the following represents the integrated rate law for a fırst-order reaction? k = Ae( Ea/RT) k1 In Ea + InA %3D k2 R 1 = kt [A]o [A]t [A]t "TAL - kt O IAl - (A), = = -kt
Which of the following represents the integrated rate law for a fırst-order reaction? k = Ae( Ea/RT) k1 In Ea + InA %3D k2 R 1 = kt [A]o [A]t [A]t "TAL - kt O IAl - (A), = = -kt
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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![### Integrated Rate Law for a First-Order Reaction
**Which of the following represents the integrated rate law for a first-order reaction?**
1. \( k = Ae^{(Ea/RT)} \)
2. \( \ln \left( \frac{k_1}{k_2} \right) = \frac{E_a}{R} \left( \frac{1}{T} \right) + \ln A \)
3. \( \frac{1}{[A]_0} - \frac{1}{[A]_t} = kt \)
4. \( \ln \left( \frac{[A]_t}{[A]_0} \right) = -kt \)
5. \( [A]_t - [A]_0 = -kt \)
### Explanation of Diagrams and Equations:
1. **Equation 1**:
- Represents the Arrhenius equation which describes the temperature dependence of reaction rates.
- \( k \) is the rate constant.
- \( A \) is the pre-exponential factor.
- \( E_a \) is the activation energy.
- \( R \) is the gas constant.
- \( T \) is the temperature in Kelvin.
2. **Equation 2**:
- Represents a form of the Arrhenius equation.
- \( k_1 \) and \( k_2 \) are rate constants at different temperatures.
- \( \ln \) represents the natural logarithm function.
- \( E_a \) is activation energy.
- \( R \) is the gas constant.
- \( T \) is the temperature.
3. **Equation 3**:
- Represents the integrated rate law for a second-order reaction.
- \( [A]_0 \) is the initial concentration of reactant A.
- \( [A]_t \) is the concentration of reactant A at time \( t \).
- \( k \) is the rate constant.
- \( t \) is the time.
4. **Equation 4**:
- Represents the integrated rate law for a first-order reaction.
- \( [A]_0 \) is the initial concentration of reactant A.
- \( [A]_t \) is the concentration of reactant A at time \( t \).
- \( k \) is the rate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F560885b1-95a6-46a1-8479-9132da42c8bd%2F9f7cf70e-e3eb-491e-93cc-7ef7d4f83264%2Ft7norfg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Integrated Rate Law for a First-Order Reaction
**Which of the following represents the integrated rate law for a first-order reaction?**
1. \( k = Ae^{(Ea/RT)} \)
2. \( \ln \left( \frac{k_1}{k_2} \right) = \frac{E_a}{R} \left( \frac{1}{T} \right) + \ln A \)
3. \( \frac{1}{[A]_0} - \frac{1}{[A]_t} = kt \)
4. \( \ln \left( \frac{[A]_t}{[A]_0} \right) = -kt \)
5. \( [A]_t - [A]_0 = -kt \)
### Explanation of Diagrams and Equations:
1. **Equation 1**:
- Represents the Arrhenius equation which describes the temperature dependence of reaction rates.
- \( k \) is the rate constant.
- \( A \) is the pre-exponential factor.
- \( E_a \) is the activation energy.
- \( R \) is the gas constant.
- \( T \) is the temperature in Kelvin.
2. **Equation 2**:
- Represents a form of the Arrhenius equation.
- \( k_1 \) and \( k_2 \) are rate constants at different temperatures.
- \( \ln \) represents the natural logarithm function.
- \( E_a \) is activation energy.
- \( R \) is the gas constant.
- \( T \) is the temperature.
3. **Equation 3**:
- Represents the integrated rate law for a second-order reaction.
- \( [A]_0 \) is the initial concentration of reactant A.
- \( [A]_t \) is the concentration of reactant A at time \( t \).
- \( k \) is the rate constant.
- \( t \) is the time.
4. **Equation 4**:
- Represents the integrated rate law for a first-order reaction.
- \( [A]_0 \) is the initial concentration of reactant A.
- \( [A]_t \) is the concentration of reactant A at time \( t \).
- \( k \) is the rate
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