OCR A-Level Chemistry: Quantitative Rates & Equilibrium

A student investigates the kinetics of the reaction between two solutions, P and Q, which react together to form a coloured product:

$\text{P} + \text{Q} \rightarrow \text{products}$P+Q→products

The student plans to use the initial-rates method to determine the order of reaction with respect to P and with respect to Q.

Describe and explain how the initial-rates method can be used to find the order with respect to each reactant. Your answer should explain how the initial rate is measured, how the concentrations are varied between experiments, and how the orders are then deduced from the results.

(6 marks)

The reaction between compounds A and B was studied at a constant temperature:

$\text{A} + \text{B} \rightarrow \text{C} + \text{D}$A+B→C+D

The initial rate was measured for three mixtures of differing initial concentrations.

Experiment	[A] / mol dm⁻³	[B] / mol dm⁻³	Initial rate / mol dm⁻³ s⁻¹
1	0.100	0.100	2.00 × 10⁻⁴
2	0.200	0.100	8.00 × 10⁻⁴
3	0.200	0.200	8.00 × 10⁻⁴

(a) Use the data to deduce the order of reaction with respect to A and with respect to B, and hence write the rate equation for this reaction. (3 marks)

(b) Calculate the value of the rate constant, $k$k, and determine its units. (3 marks)

The decomposition of a compound X in solution was followed at constant temperature by removing samples and titrating to find [X]. The results are shown below.

Time / s	0	100	200	300	400
[X] / mol dm⁻³	0.800	0.400	0.200	0.100	0.050

(a) Use the idea of half-life to show that the decomposition of X is first order. (3 marks)

(b) Calculate the rate constant, $k$k, for the decomposition, and state its units. Use the relationship $k = \frac{\ln 2}{t_{1/2}}$k=t1/2​ln2​. (2 marks)

A gas-phase reaction has the overall equation:

$\text{NO}_2 + \text{CO} \rightarrow \text{NO} + \text{CO}_2$NO2​+CO→NO+CO2​

Experiments show that the rate equation is:

$\text{rate} = k[\text{NO}_2]^2$rate=k[NO2​]2

Two mechanisms have been proposed.

Mechanism 1 (single step): $\text{NO}_2 + \text{CO} \rightarrow \text{NO} + \text{CO}_2$NO2​+CO→NO+CO2​

Mechanism 2 (two steps): $\text{Step 1: } \text{NO}_2 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{NO} \quad (\text{slow})$Step 1: NO2​+NO2​→NO3​+NO(slow) $\text{Step 2: } \text{NO}_3 + \text{CO} \rightarrow \text{NO}_2 + \text{CO}_2 \quad (\text{fast})$Step 2: NO3​+CO→NO2​+CO2​(fast)

Use the rate equation to decide which mechanism is consistent with the experimental data. Justify your choice fully. (5 marks)

The rate constant for a reaction was measured at several temperatures. A graph of $\ln k$lnk against $\frac{1}{T}$T1​ (with $T$T in kelvin) gave a straight line of gradient $-6.00 \times 10^{3}\ \text{K}$−6.00×103 K.

The Arrhenius equation in logarithmic form is:

$\ln k = \ln A - \frac{E_a}{RT}$lnk=lnA−RTEa​​

(a) Use the gradient to calculate the activation energy, $E_a$Ea​, for the reaction. Give your answer in kJ mol⁻¹. ($R = 8.31\ \text{J mol}^{-1}\,\text{K}^{-1}$R=8.31 J mol−1K−1) (3 marks)

(b) State what the intercept of this graph represents. (1 mark)

This question is about rate equations and reaction mechanisms.

(a) State what is meant by the order of reaction with respect to a given reactant. (1 mark)

(b) A reaction between substances E and F is first order in E and second order in F. Write the rate equation for this reaction. (1 mark)

(c) State what is meant by the rate-determining step of a multi-step reaction. (1 mark)