Researchers record half-life data for the aqueous decomposition of reactant D at 20 °C

CHEMISTRY · Multi-part · A Level · Chemistry · Rate equations · Rate equations

Problem

Researchers record half-life data for the aqueous decomposition of reactant D at 20 °C, including estimated measurement uncertainties.

Run	[D]₀ (mol L⁻¹)	± σ([D]₀)	t₁/₂ (s)	± σ(t₁/₂)
1	0.150	0.002	36.2	0.5
2	0.300	0.002	18.1	0.4
3	0.600	0.003	9.0	0.3

Assume a single step mechanism and constant temperature. (1) Use the data, including uncertainties, to determine the overall reaction order with respect to D. Clearly show how the experimental ratios support your conclusion within the stated uncertainties. (2) For each run, calculate the rate constant

k

with appropriate units. Propagate the given uncertainties to obtain σ(k) for each run. (3) Compute the average value of

k

from the three runs and its combined standard uncertainty. Report

k_{avg} \pm σ_{avg}

with units. (4) Discuss one specific procedural modification to the experimental design that would most effectively reduce the uncertainty in the determined value of

k

. Justify your choice.

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