A6. At 600 K, SO 2 Cl decomposes with a rate constant 1.02 × 10 –6 s–1 . Theactivation energy for this decomposition is 210 kJ mol –1 . According to theArrhenius Equation, which ONE of the following statements is CORRECT?Assume that the frequency factor does not change with temperature.(A) At 500 K, the rate constant is lower than it is at 600 K and theactivation energy is higher than at 600 K..(B) At 500 K, the rate constant is the same as it is at 600 K and theactivation energy is higher than at 600 K..(C) At 500 K, the rate constant is lower than it is at 600 K and theactivation energy is lower than at 600 K.(D) At 500 K, the rate constant is lower than it is at 600 K and theactivation energy is the same as it is at 600 K.(E) At 500 K, the rate constant is higher than it is at 600 K and theactivation energy is the same as it is at 600 K
Question
A6. At 600 K, SO 2 Cl decomposes with a rate constant 1.02 × 10 –6 s–1 . Theactivation energy for this decomposition is 210 kJ mol –1 . According to theArrhenius Equation, which ONE of the following statements is CORRECT?Assume that the frequency factor does not change with temperature.(A) At 500 K, the rate constant is lower than it is at 600 K and theactivation energy is higher than at 600 K..(B) At 500 K, the rate constant is the same as it is at 600 K and theactivation energy is higher than at 600 K..(C) At 500 K, the rate constant is lower than it is at 600 K and theactivation energy is lower than at 600 K.(D) At 500 K, the rate constant is lower than it is at 600 K and theactivation energy is the same as it is at 600 K.(E) At 500 K, the rate constant is higher than it is at 600 K and theactivation energy is the same as it is at 600 K
Solution
Step 1: Understand the problem
The problem is asking us to determine the effect of a decrease in temperature on the rate constant and the activation energy of a reaction, according to the Arrhenius equation.
Step 2: Understand the Arrhenius equation
The Arrhenius equation is given by:
k = Ae^(-Ea/RT)
where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
Step 3: Understand the effect of temperature on the rate constant and the activation energy
According to the Arrhenius equation, the rate constant k increases with increasing temperature, because the exponential term becomes larger (more molecules have the necessary energy to overcome the activation energy). Therefore, if the temperature decreases from 600 K to 500 K, the rate constant should decrease.
The activation energy Ea is a property of the reaction and does not change with temperature. Therefore, the activation energy at 500 K is the same as at 600 K.
Step 4: Choose the correct answer
The correct answer is (D) At 500 K, the rate constant is lower than it is at 600 K and the activation energy is the same as it is at 600 K.
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