Reaction Kinetics: Question 6

Worked solution

Step 1: Reaction 1. Constant gradient

A straight-line graph of $[\text{R}]$ against time, with a constant gradient, means that $[\text{R}]$ decreases by the same amount every second. The rate of loss of R is constant and does not depend on how much R is left. This is the defining feature of a zero-order reaction with respect to R: $\text{rate} = k[\text{R}]^0 = k$.

Step 2: Reaction 2. Constant half-life

A curve for which the time taken for $[\text{R}]$ to halve is always the same, no matter what the starting concentration for that stage is, has a constant half-life. A constant half-life, independent of concentration, is the defining feature of a first-order reaction with respect to R.

Step 3: Reaction 3. Increasing half-life

A curve for which the half-life becomes progressively longer as the reaction proceeds (i.e. as $[\text{R}]$ falls) is characteristic of a second-order reaction. As $[\text{R}]$ decreases, the rate ($\propto [\text{R}]^2$) falls away much more steeply than for a first-order reaction, so it takes longer and longer for the remaining R to halve.

Step 4: Matching to the options

Reaction 1 = zero order, Reaction 2 = first order, Reaction 3 = second order, this matches option A.

• B swaps the zero- and first-order descriptions.
• C and D both misassign the second-order (increasing half-life) behaviour to the wrong reaction.

Final answer

• $\boxed{\text{A}}$. Reaction 1 zero order, Reaction 2 first order, Reaction 3 second order.