Q: A reaction has a rate constant $$k_1 = 2.14$$ \times $$10^{-4} M$^{-1}s$^{-1} at$$ $$T_1 = 312.15$ K and an activation energy E_a = 80.4$ kJ/mol. What is the rate constant k_2$ at T_2$ = 334.15 K$$? (Use $$R = 8.314 J/$$mol·K)

$$k_2 = 1.644$$ \times $$10^{-3} M$^{-1}s$^{-1}$$

Question 1

Which of the following statements best describes the role of activation energy ($$E_a) in a $$chemical reaction, as illustrated in the reaction coordinate diagrams?

Accepted Answer

Activation energy is the minimum energy required for reactants to reach the transition state and form the activated complex.

Question 2

According to the Arrhenius equation $$k = Ae$$^{-E_a/(RT)}$$, what happens to the rate constant k$ when the activation energy E_a$ increases, assuming all other factors remain constant?

Accepted Answer

The rate constant $$k$$ decreases.

Question 3

Which of the following best explains why increasing temperature increases the rate of a chemical reaction, as shown in the thermal energy distribution diagram?

Accepted Answer

Higher temperature increases the number of molecules with energy greater than $$E_a$$, allowing more successful collisions.

Question 4

In an exothermic reaction, as shown in the reaction coordinate diagrams, which statement is correct regarding the energy of products and reactants?

Accepted Answer

The energy of the products is lower than the energy of the reactants.

Question 5

Given the Arrhenius equation $$k = Ae$$^{-E_a/(RT)}$$, which factor is most responsible for the exponential increase in reaction rate with temperature?

Accepted Answer

The exponential factor $$e^{-E_a/(RT)}.$$

Question 6

A reaction has a rate constant $$k_1 = 2.14$$ 	imes $$10^{-4} M$^{-1}s$^{-1} at$$ $$T_1 = 312.15$ K and an activation energy E_a = 80.4$ kJ/mol. What is the rate constant k_2$ at T_2$ = 334.15 K$$? (Use $$R = 8.314 J/$$mol·K)

Accepted Answer

$$k_2 = 1.644$$ 	imes $$10^{-3} M$^{-1}s$^{-1}$$

Question 7

Which of the following is true about the frequency factor $$A in $$the Arrhenius equation?

Accepted Answer

It is the product of collision frequency and orientation probability.

Question 8

If a reaction has a high activation energy, what can be inferred about its rate at a given temperature?

Accepted Answer

The reaction rate will be slow.

Question 9

Which equation allows you to determine the activation energy $$E_a$$ from two measurements of the rate constant at different temperatures?

Accepted Answer

$$\ln \frac{k_2$}{k_1$} = \frac{E_a}{R} \left( \frac{1}{T_1$} - \frac{1}{T_2$} \right)$$

Question 10

In the context of chemical kinetics, what does the 'activated complex' refer to?

Accepted Answer

A transition state with partially broken and partially formed bonds.

Question 11

Which of the following best describes the effect of a catalyst on the activation energy and reaction rate?

Accepted Answer

A catalyst decreases the activation energy, increasing the reaction rate.

Question 12

A plot of $$\ln k$$ versus $$1/T$$ yields a straight line. What does the slope of this line represent?

Accepted Answer

The negative activation energy divided by the gas constant, $$-E_a/R.$$

Question 13

If the exponential factor $$e^{-E_a/(RT)} in $$the Arrhenius equation approaches zero, what does this imply about the reaction rate?

Accepted Answer

The reaction rate is very slow.

Question 14

Which scenario would result in the largest rate constant $$k$$ for a reaction, according to the Arrhenius equation?

Accepted Answer

Low activation energy and high temperature.

Question 15

In a laboratory experiment, you plot $$\ln k$$ versus $$1/T$$ and obtain a slope of $$-9668.5 K. $$What is the activation energy $$E_a in kJ/$$mol? (Use $$R = 8.314 J/$$mol·K)

Accepted Answer

$$E_a = 80.4 kJ/$$mol

Question 16

Which of the following is NOT a requirement for a successful chemical reaction according to collision theory?

Accepted Answer

Molecules must collide instantaneously.

Question 17

For an endothermic reaction, as shown in the reaction coordinate diagrams, which statement is correct regarding the energy of products and reactants?

Accepted Answer

The energy of the products is higher than the energy of the reactants.

Question 18

A reaction has $$k_1 = 7.90$$ 	imes $$10^{-2} M$^{-1}s$^{-1} at$$ $$T_1 = 781.15$ K and k_2$ = 2.40 	imes 10$$^{-1}$$ M$$^{-1}$$s$$^{-1}$$ at T_2$ = 813.15 K. $$What is the activation energy $$E_a in kJ/$$mol? (Use $$R = 8.314 J/$$mol·K)

Accepted Answer

$$E_a = 183 kJ/$$mol

Question 19

Which of the following best describes the effect of increasing the frequency factor $$A in $$the Arrhenius equation?

Accepted Answer

It increases the rate constant $$k by $$increasing the number of properly oriented collisions.

Chemical Kinetics: Temperature and Reaction Rates (Arrhenius Equation)

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