CI abcde: Kinetics: rates & orders of reactions; Arrhenius equation

Question 1

Why does increasing the concentration of a reactant not necessarily mean that the rate of reaction will increase?

Answer 1

The reactant may not be involved in the rate-determining step.

Question 2

What influences how fast a rate-determining step is?

Answer 2

Its activation enthalpy.

Question 3

2H₂O₂ → 2H₂O + O₂

0.01 moles of oxygen are formed per second. What is the rate in terms of hydrogen peroxide?

Answer 3

- 0.02 mol s^-1

Question 4

Rate = k[H₂O₂][catalase] at temperature T.

What is the unit of the rate constant?

Answer 4

k = rate / product of concentrations

mol dm^-3 s^-1

(mol dm^-3)(mol dm^-3)

So unit of k = dm³ mol^-1 s^-1

Write positive indices first by convention

Question 5

Experimental evidence showed the rate of a reaction is given by the following equation:

rate = k[S₂O₈^2-][I^-]

What is the order of the reaction:

• With respect to each of the reactants?
• Overall?

Answer 5

• First order with respect to S₂O₈^2-
• First order with respect to I^-
• Second order overall (add the powers)

Question 6

What is the unit of the rate constant for zero order reactions?

Answer 6

mol dm^-3 s^-1

Question 7

What is the unit of the rate constant for first order reactions?

Answer 7

s^-1

Question 8

What is the unit of the rate constant for second order reactions?

Answer 8

dm³ mol^-1 s^-1

Question 9

This is the Arhenius equation:

k = Ae^-E_a/RT

What is represented by each symbol?

Answer 9

k, rate constant

A, frequency factor

e, the constant

E_a, activation enthalpy

R, gas constant

T, temperature in Kelvin

Question 10

k = Ae^-E_a/RT

Prove that the Arrhenius equation can be used to plot a straight line graph. State its gradient and y-intercept.

Answer 10

Take natural log of both sides (on data sheet)

lnk = -E_a/RT + lnA

lnk = -E_a/R x 1/T + lnA

Since k and T are the only variables, this is equivalent to y = mx + c

Plot lnk against 1/T

Gradient = -E_a/R and y-intercept = lnA

Question 11

What is the unit of A in the Arrhenius equation?

Answer 11

The same as that of k.

Question 12

What is the magnitude of the change in rate of a reaction with activation energy 50 kJ mol^-1 when the temperature is increased from 20^oC to 30^oC?

Answer 12

In both cases, k = [X]^m[Y]ⁿ so k is only factor affecting rate; k ∝ rate

Convert E_a into J (unit of gas constant) and T into K.

k₁ = A e^{-50,000 / 8.314 x 293} = 1.2 x 10⁹ A

k₂ = A e^{-50,000 / 8.314 x 303} = 2.4 x 10^-9 A

A is a constant, so number of collisions + therefore rate is multiplied by approx. 2

Question 13

Which statement about the Arhenius equation is correct?

1. A plot of lnk against T gives a straight line
2. When T is very large, ln k almost equals A
3. E_a is the gradient of a plot of ln k against 1/T
4. A plot of k against 1/T gives a straight line

Answer 13

2

1. Should be 1/T
2. lnk = -E_a/R x 1/T + lnA = -E_a/RT + lnA so, as T → ∞, -E_a/RT → 0
3. Should be -E_a/R
4. Should be lnk

Question 14

Suggest 5 methods of analysis which could be used to measure the rate of a reaction.

Answer 14

• Titration
• pH
• Colorimetry
• Volume of gas evolved
• Mass change

Question 15

How does quenching work?

Answer 15

• Sample isolated from reaction mixture
• Chemical added which stops reaction (e.g. neutralises a catalyst)
• Sample titrated to find conc. of a reactant/product

Question 16

To work out the rate equation for a reaction, you need to vary the concentration of the reactants one at a time.

In what 2 ways could you ensure that you are investigating the effect of a single reactant?

Answer 16

• Run one experiment with a given concentration of one reactant. Have other in excess so that its concentration does not change significantly
• Run several experiments with different concentrations of one reactant. Keep concentration of other reactant constant

Question 17

Explain how the initial rate method can be used to determine the order of a reaction with respect to one reactant.

Answer 17

• Run several experiments with different concentrations of one reactant. Keep concentration of other reactant(s) constant
• Measure conc of first reactant throughout
• For each, plot concentration against time, then take gradient of tangent at origin: initial rate
• Plot initial rate against concentration:
  
  • Flat line = 0 order wrt this reactant
  • Straight line with gradient > 0: 1st order wrt this reactant
  • If initial rate against conc² is straight line with gradient > 0: 2nd order wrt this reactant

Question 18

Explain how reaction time can be used to determine the order of a reaction with respect to one reactant.

Answer 18

• Run several experiments with different concentrations of one reactant. Keep concentration of other reactant(s) constant
• For each conc, measure time taken to form a small, fixed amount of a product
• Rate = amount of product / time. For given amount, initial rate ∝ 1/t
• Plot 1/t against concentration:
  
  • Flat line = 0 order wrt this reactant
  • Straight line with gradient > 0: 1st order wrt this reactant
  • If 1/t against conc² is straight line with gradient > 0: 2nd order wrt this reactant

Question 19

Explain how half-lives can be used to determine whether a reaction is first order with respect to one reactant.

Answer 19

• Run one experiment with a given concentration of one reactant. Have other(s) in excess
• Measure concentration of reactant of interest throughout reaction
• Plot concentration against time
• Find 3 half-lives: time for concentration to halve
• Constant half-life indicates reaction is 1st order with respect to reactant of interest

Question 20

Answer 20

B

A: gradient is constant, so rate with respect to A is constant; [A] doesn’t affect rate so 0, not 1st, order

C: insufficient information to know

D: they are

Question 21

Which of these graphs is a straight line for the first order reaction Z → products?

1. [Z] against time
2. rate against [Z]
3. ln k against 1/T

• A 1, 2 and 3
• B only 1 and 2
• C only 2 and 3
• D only 1

Answer 21

C

Not 1 as there is constant deceleration, not constant decrease.

Question 22

A reaction is first order with respect to a catalyst, Y. What is true about a graph of [Y] against time?

1. It will be a curve going downwards with constant half life
2. It will be a straight line going downwards
3. It will be a straight line parallel with the x-axis
4. It will be a curve rising with decreasing rate

Answer 22

3

(Catalyst, so not used up during reaction)

Question 23

H₂O₂ + 2H⁺ + 2I^- → 2H₂O + I₂

Rate = k [H₂O₂] [I^-]

Discuss the two mechanisms in terms of the orders of reaction and the individual steps. (4)

Mechanism 1

1. H₂O₂ + I^- → H₂O + IO^- (slow)
2. IO^- + 2H⁺ + I^-→ I₂ + H₂O (fast)

Mechanism 2

1. H₂O₂ + I^- → H₂O + IO^- (fast)
2. H⁺ + IO^- →HIO (slow)
3. H⁺ + HIO → H₂IO⁺ (fast)
4. H₂IO⁺ + I^- → I₂ + H₂O (fast)

Answer 23

• Mechanism 1 has correct slow step not involving H⁺
• The slow step would be first order with respect to H₂O₂ and I^-
• Mechanism 2 has all two-body (AW) collisions
• One of:
  
  • Slow step in 2 would give 1st order with respect to all 3 reagents
  • Fast step of 1 very unlikely as 4 particles collide