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Q1

Consider the reaction: $\displaystyle H_2 +\ Br_2 \rightarrow 2HBr$

Express the rate of reaction in terms of the rate of change of the following species, i.e. $\displaystyle \frac{d[X]}{dt}$

i. H₂

ii. Br₂

iii. HBr

Q2

Consider the reaction:

$\displaystyle 2NO_2 \rightarrow N_2O_4$

Express the rate of reaction in terms of the rate of change of the following species. i. NO₂

ii. N₂O₄

Q3

Coming soon

Q4

A first order reaction can described by the rate equation: $\displaystyle rate=k[X]$

Derive an expression for the half life of [X] in terms of k and show it is time-independent. [The half life of reactant, $\displaystyle t_{\frac{1}{2}}$ is defined as the time taken for it to drop to half its initial concentration]

Q5

If a reaction is believed to be 1st order with respect to [X], what graph should be plotted to show confirm this? How could the rate constant be determined?

[Hint: a relationship which produces a straight line is the easiest to verify.]

Q6

Sketch plots of rate against [X] and rate against time. Explain the form of your plots.

Q7

A second order reaction can described by the rate equation: $\displaystyle rate=k[X]^2$

Derive an expression for the half life of X in terms of k and confirm that it is time-dependent.

Q8

What graph should be plotted to confirm a reaction is 2nd order with respect to X? How could the rate coefficient be determined?

Q9

Sketch a plot of rate against X. Explain the form of your plot.

Q10

Consider a general reaction $\displaystyle X +\ X \rightarrow Z$

Derive an expressions for [Z] as a function of time the inital concentration of X.

Q11

A reaction $\displaystyle X \rightarrow Z$ has a rate which can be written as $\displaystyle rate = k[X]$ with rate constant $\displaystyle k = 3.2 \times 10^{-3} s^{-1}$

How long will it take for: i. [X] to reach $\frac{1}{16}$ of its original value?

ii. [X] to reach $\frac{1}{e}$ of its original value (this is called the lifetime, $\tau$ , of the reactant)?

iii. [Z] to reach $\frac{3}{4}$ of its final value?

Q12

A compound has a concentration of 1×10⁻³ mol dm^-3. A solution of this compound has a path length of 2 cm and when it is irradiated the incident radiation is 7.14 times more intense than the radiation exiting the solution. What is the species’ molar extinction coefficient? Provide the answer in units of mol⁻¹ dm³ cm^-1.

Q13

How would the pre-exponential factor of a rate coefficient be determined from an appropriate plot?

Q14

Convert a rate of 12 mol dm^-3s^-1 into molecules cm^-3 min^-1

Q15

What are the units of the rate constants for the following rate equations if concentration is measured in mol dm^{-3(time always in seconds)?}

i. $rate=k[A][B]^2$

ii. $rate=k[A]^2[B]^{\frac{5}{2}}$

Q16

For an exothermic, single step reaction the enthalpy change of a reaction is denoted $\Delta H$ and the activation energy of the forward reaction $E_{a1}$ . Express the activation energy of the reverse reaction, $E_{a-1}$ , in terms of $\Delta H$ and $E_{a1}$ .

Q17

For the system described in question 16 write down expressions for the following in terms of $E_{a1}$ and $\Delta H$ :

i. the rate constant of the forward reaction, $k_{1}$

ii. the rate constant of the reverse reaction <img src=”https://render.githubusercontent.com/render/math?math=k_{-1}

Q18

Write down a differential equation describing the rate of change of [O] for the 4 reactions in the Chapman cycle.

Q19

Consider a reaction scheme:

$A \rightarrow B \rightarrow C$

with rate constants k₁ and k₂ for the first and second reactions.

It so happens that $k_2 \gg k_1$ (i.e. B is in steady state) and [A]=[A]₀ when t=0.

Derive expressions for [A],[B] & [C] in terms of [A]₀, t, k₁ and k₂.

Q20

Now consider the situation in the previous question with the additional reactions:

$B \rightarrow A$ and $C \rightarrow B$

These have rate constants k_-1 and k_-2 respectively.

Write expressions for the rates of change of [A],[B] & [C]. In the special case where [B] is in steady state, derive an expression for its concentration.