Topic 11: Kinetics

Rate commonly has units mol dm$^{-3}$ s$^{-1}$. Rearrange the measured rate equation to find $k$, then derive its units: zero order gives mol dm$^{-3}$ s$^{-1}$; first order gives s$^{-1}$; second order gives dm$^3$ mol$^{-1}$ s$^{-1}$.

A 100 mg dose with a 20 min half-life undergoes 12 half-lives in 4 h. The mass is $100(1/2)^{12}=0.0244$ mg, or 24.4 μg.

The measured signal must change monotonically with the chosen reactant or product and be fast to record compared with the reaction. State what is measured, how it relates to concentration, the sampling frequency and the main source of loss or delay.

A clock method uses the time to reach the same small, fixed amount of reaction. If the clock reagent is small compared with the main reactants, their concentrations change little before the endpoint, so $1/t$ is proportional to initial rate.

Keep total volume, temperature and all non-tested initial concentrations constant. Start timing at consistent mixing and use the same endpoint; otherwise $1/t$ compares different extents rather than rates.

Compare runs in which only one concentration changes. If concentration changes by factor $f$ and rate by factor $g$, solve $g=f^m$. When two concentrations change together, first account for the known order of one before isolating the other.

A concentration–time gradient gives rate, so compare gradients at chosen concentrations. A rate–concentration graph displays the dependence directly. State both the observed factor/shape and the resulting order.

The evidence supports a slow acid-catalysed formation of the enol from propanone, involving propanone and $\mathrm{H^+}$, followed by fast reaction of the enol with iodine. Iodine is absent from the rate-determining process, and $\mathrm{H^+}$ is regenerated.

Follow iodine loss by timed aliquots and titration, or by calibrated colorimetry. Use iodine in the smaller amount so propanone and acid remain nearly constant during a run.

If the observed rate is first order in H$_2$O$_2$, a slow elementary step containing one H$_2$O$_2$ molecule is consistent; a slow collision between two H$_2$O$_2$ molecules predicts second order and is inconsistent.

For an overall $\mathrm{A+B+C ightarrow P}$ reaction with $ext{rate}=k[\mathrm{A}][\mathrm{B}]$, a possible scheme is slow $\mathrm{A+B ightarrow X}$ followed by fast $\mathrm{X+C ightarrow P}$. Adding the steps cancels X and gives the overall equation.

Work from both ends: use the rate law to constrain the slow step, then add fast steps needed to account for the remaining overall reactants and products. Reject any scheme that leaves an intermediate uncancelled.

If doubling [RX] doubles rate and doubling [OH$^-$] also doubles rate, the reaction is first order in each and supports S$_N$2. If changing [OH$^-$] has no effect while rate follows [RX], the evidence supports S$_N$1.

Use $R=8.31$ J K$^{-1}$ mol$^{-1}$, so the calculated $E_a$ is initially in J mol$^{-1}$. The Arrhenius line has a negative gradient but activation energy is reported as a positive barrier.

A finely divided catalyst exposes more active surface area, so more reactant particles can be adsorbed at once. The catalyst is heterogeneous because solid and gas are different phases, and separation from the surface stops this catalytic route.

Thiosulfate removes iodine as it forms; it does not slow the main iodine-producing reaction. Once thiosulfate is exhausted, iodine remains and forms the blue-black starch complex. Keep temperature, total volume and non-tested concentrations constant.

Use consistent mixing/start time, repeat each condition and compare concordant endpoint times. In the aliquot method, sampling time and complete quenching are critical; in the clock, subjective colour judgement and delay in mixing affect precision.

At a fixed endpoint, the same small amount reacts in each run, so relative rate is proportional to $1/t$. Any constant proportionality factor changes the intercept of the Arrhenius plot but not its gradient.

Maintain temperature during each run, use the same observer/endpoint and minimise delay between mixing and timing. Include all valid points in a best-fit line and investigate rather than silently discard an anomalous result.