Temperature and Rate - Arrhenius Equation - UNSOLVED PRACTICE SET
Chapter: Chemical Kinetics | Topic: Temperature and Rate Arrhenius Equation
TEMPERATURE AND RATE - ARRHENIUS EQUATION - UNSOLVED PRACTICE SET
Topic: Temperature and Rate Arrhenius Equation
Multiple Choice Questions
Q1. The Arrhenius equation is:
- k = A·e^(Ea/RT)
- k = A·e^(-Ea/RT)
- k = A/Ea·RT
- k = A + Ea/RT
Q2. In the Arrhenius equation, 'A' represents:
- Activation energy
- Frequency factor or pre-exponential factor
- Rate constant at zero temperature
- Gas constant
Q3. The logarithmic form of the Arrhenius equation is:
- ln k = ln A + Ea/RT
- ln k = ln A – Ea/RT
- ln k = ln A × Ea/RT
- ln k = Ea/RT – ln A
Q4. A plot of ln k vs. 1/T for a reaction gives:
- A straight line with a positive slope
- A straight line with a negative slope
- A curve
- A horizontal line
Q5. The slope of the plot of log k vs. 1/T is equal to:
- –Ea/2.303R
- Ea/2.303R
- –Ea/R
- Ea/R
Q6. If the temperature of a reaction is increased from T₁ to T₂, the rate constant:
- Always decreases
- Always increases
- Remains unchanged
- May increase or decrease depending on the reaction
Short Answer Questions
Q7. State the Arrhenius equation and explain the meaning of each term.
Q8. How can you determine the activation energy of a reaction experimentally using the Arrhenius equation?
Q9. The rate constant of a reaction doubles when the temperature is increased by 10°C. Is this always true? Explain the limitations of this rule of thumb.
Q10. A plot of ln k vs. 1/T gives a straight line with slope = –5000 K. Calculate the activation energy of the reaction. (R = 8.314 J K⁻¹ mol⁻¹)
Q11. Why does increasing temperature increase the rate of reaction? Explain using the Arrhenius concept.
Q12. The activation energy of a reaction is 50 kJ/mol. At what temperature will the rate constant be twice its value at 300 K? (Use the Arrhenius equation conceptually—set up the equation without solving numerically if you prefer.)
Long Answer Questions
Q13. Derive the two-point form of the Arrhenius equation:
ln(k₂/k₁) = (Ea/R)((T₂ – T₁)/(T₁T₂))
Explain how this can be used to calculate activation energy when rate constants at two different temperatures are known.
Q14. (a) Explain the effect of temperature on the rate constant of a reaction using the Arrhenius equation.
(b) The rate constant of a reaction is 1.0 × 10⁻³ s⁻¹ at 300 K and 4.0 × 10⁻³ s⁻¹ at 320 K. Calculate the activation energy. (R = 8.314 J K⁻¹ mol⁻¹)
Q15. (a) What is the significance of the frequency factor (A) in the Arrhenius equation? How is it related to collision theory?
(b) The activation energy for the decomposition of a compound is 100 kJ/mol. At 300 K, the rate constant is 2.0 × 10⁻⁵ s⁻¹. Calculate the rate constant at 320 K using the Arrhenius equation.
Numerical / Application-Based Problems
Q16. For a certain reaction, the rate constants at 300 K and 320 K are 2.5 × 10⁻³ s⁻¹ and 1.0 × 10⁻² s⁻¹, respectively.
(a) Calculate the activation energy (Ea).
(b) Calculate the pre-exponential factor A.
(c) Calculate the rate constant at 340 K.
[Given: R = 8.314 J K⁻¹ mol⁻¹]
Q17. The following data were obtained for a reaction:
| Temperature (K) | Rate Constant (s⁻¹) |
|---|---|
| 300 | 1.0 × 10⁻⁴ |
| 310 | 2.5 × 10⁻⁴ |
| 320 | 6.0 × 10⁻⁴ |
(a) Plot log k vs. 1/T (describe how you would do this).
(b) From the slope of this plot, calculate the activation energy.
(c) Calculate the pre-exponential factor A.
(d) Predict the rate constant at 330 K.
Q18. In a school science project, a student investigates why milk sours faster in summer than in winter. She learns that the souring of milk is a chemical reaction with an activation energy of 75 kJ/mol.
(a) Explain using the Arrhenius equation why the reaction is faster at higher temperatures.
(b) If the rate constant at 298 K (25°C) is 1.2 × 10⁻³ day⁻¹, calculate the rate constant at 308 K (35°C).
(c) By what factor does the rate increase? What does this mean practically for keeping milk fresh?
(d) Suggest two ways (other than refrigeration) to slow down the souring of milk based on chemical kinetics principles.