14.3.3 Using the Arrhenius Equation

Question 1

Using the Arrhenius Equation

Answer 1

• The Arrhenius equation can be rewritten for two temperatures, allowing for comparisons between those two temperatures.
• The Arrhenius equation is useful for predicting the rate constant (k) of a reaction at a given temperature.
• The activation energy (E a ) can be calculated when the rate constants are known at two different temperatures.

Question 2

note

Answer 2

• The Arrhenius equation can be rewritten for two temperatures, allowing for comparisons between those two temperatures.
• This is done by subtracting the Arrhenius equation for a
  temperature T 1 from the Arrhenius equation for a temperature T 2 . This eliminates the frequency factor (A).
• The Arrhenius equation is useful for predicting the rate
  constant (k) of a reaction at a given temperature.
• Problem: For the reaction 2HI(g) –8 H 2 (g) + I 2 (g), the rate –1 –1 constant (k 1 ) is 2.55 x 10 M s at 650 K and the activation energy (Ea) is 168 kJ/mol. What is the rate constant (k 2 ) at 700 K?
• Plugging the given information into the form of the Arrhenius equation for two temperatures yields the second rate constant (k 2 ).
• The activation energy (E a ) can be calculated when the rate constants are known at two different temperatures.
• Problem: For the reaction CO(g) + Cl 2 (g) COCl 2 (g), at 250 ̊C the reaction is 1.5 x 103 times as fast as the same reaction at 150 ̊C. Calculate the activation energy (E a ).
• First, the given temperatures must be converted to kelvins using the formula T( ̊C) + 273 K = T(K).
• Plugging the given information into the form of the Arrhenius equation for two temperatures yields the activation energy (E a ).

Question 3

According to the Arrhenius equation, how does temperature affect the rate constant?

Answer 3

The rate constant increases as the temperature increases.

Question 4

Which of the following is the correct Arrhenius equation?

Answer 4

ln k2 / k1 = −Ea / R (1 / T2−1 / T1 )

Question 5

Which of the following is not a constant in the Arrhenius equation?

Answer 5

T

Question 6

Which of the following is true regarding the variable T in the Arrhenius equation?

Answer 6

The temperature values must be in units of Kelvin.

Question 7

Which of the following can NOT be calculated using the Arrhenius equation?

Answer 7

The concentration of products at a given temperature

Question 8

Given the following information, find the activation energy for the decomposition of acetaldehyde.

k1 = 1.05 × 10−3 M −1/2s−1 at 759 K
k2 = 2.14 × 10−2 M −1/2s−1 at 836 K

Answer 8

2.06 × 10^5 J / mol

Question 9

In 1889, Svante Arrhenius demonstrated that rate constants of many chemical reactions vary with what?

Answer 9

temperature

Question 10

The familiar form for the Arrhenius equation for two different absolute temperatures T1 and T2 is:
ln k2 / k1 = −Ea / R (1 / T2 − 1 / T1 )
Equations relating several parameters can usually be expressed in any of several algebraically equivalent expressions.
Which of the following is an algebraically equivalent expression of the Arrhenius equation?

Answer 10

ln k2 / k1 = Ea / R (1 / T1 − 1 / T2 )

Question 11

In the reaction, 2HI(g) → H2(g) + I2(g), the activation energy is 184 kJ / mol and the rate constant is 2.55 × 10−8 m−1s−1 at 650 K. What is the rate constant at 750 K?

Answer 11

2.39 × 10^−6 m−1s−1

Question 12

Arrhenius demonstrated that temperature of many chemical reactions affects what?

Answer 12

rate constants