a reaction has a rate constant of 33 s⁻¹ at 298k and a rate constant of 45 s⁻¹ at 675 k. what is the…

a reaction has a rate constant of 33 s⁻¹ at 298k and a rate constant of 45 s⁻¹ at 675 k. what is the activation energy of this reaction? a 4800 j/mol b 700 j/mol c 1400 j/mol d 20 j/mol question 8 the rate constant for the decay of radon - 222 is 0.181 day⁻¹. what is the half - life of radon - 222? a 3.83 days b 2.61 days c 0.181 days d 1.25 days question 9 which of the following statements best describes how catalysts work? a a catalyst changes the entropy of the reaction by allowing the reaction to happen via a different mechanism. b a catalyst decreases the activation energy by allowing the reaction to happen via a different mechanism. c a catalyst decreases the activation energy by providing a source of heat. d a catalyst changes the entropy of the reaction by providing a source of heat.

a reaction has a rate constant of 33 s⁻¹ at 298k and a rate constant of 45 s⁻¹ at 675 k. what is the activation energy of this reaction? a 4800 j/mol b 700 j/mol c 1400 j/mol d 20 j/mol question 8 the rate constant for the decay of radon - 222 is 0.181 day⁻¹. what is the half - life of radon - 222? a 3.83 days b 2.61 days c 0.181 days d 1.25 days question 9 which of the following statements best describes how catalysts work? a a catalyst changes the entropy of the reaction by allowing the reaction to happen via a different mechanism. b a catalyst decreases the activation energy by allowing the reaction to happen via a different mechanism. c a catalyst decreases the activation energy by providing a source of heat. d a catalyst changes the entropy of the reaction by providing a source of heat.

Answer

Explanation:

Question 7

Step1: Recall Arrhenius equation

The Arrhenius equation in two - point form is $\ln\left(\frac{k_2}{k_1}\right)=\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$, where $k_1$ and $k_2$ are rate constants, $T_1$ and $T_2$ are temperatures, $E_a$ is the activation energy and $R = 8.314\ J/(mol\cdot K)$. Given $k_1 = 33\ s^{-1}$, $T_1=298\ K$, $k_2 = 45\ s^{-1}$, $T_2 = 675\ K$.

Step2: Rearrange for $E_a$

$E_a=R\times\ln\left(\frac{k_2}{k_1}\right)\div\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$. First, calculate $\frac{1}{T_1}-\frac{1}{T_2}=\frac{T_2 - T_1}{T_1T_2}=\frac{675 - 298}{298\times675}=\frac{377}{298\times675}\approx1.89\times10^{-3}\ K^{-1}$. Then, $\ln\left(\frac{k_2}{k_1}\right)=\ln\left(\frac{45}{33}\right)\approx\ln(1.364)\approx0.311$. So, $E_a = 8.314\times0.311\div(1.89\times10^{-3})\approx1400\ J/mol$.

Question 8

Step1: Recall half - life formula for first - order reaction

For a first - order reaction, the half - life formula is $t_{1/2}=\frac{\ln(2)}{k}$. Given $k = 0.181\ day^{-1}$.

Step2: Calculate half - life

$t_{1/2}=\frac{\ln(2)}{0.181}=\frac{0.693}{0.181}\approx3.83\ days$.

Question 9

Step1: Understand catalyst concept

A catalyst works by providing an alternative reaction mechanism with a lower activation energy. It does not change the entropy of the reaction by providing heat.

Answer:

Question 7: C. 1400 J/mol Question 8: A. 3.83 days Question 9: B. A catalyst decreases the activation energy by allowing the reaction to happen via a different mechanism.