For the gas-phase reaction at 300°C: C2F4 → 1/2 cyclo-C4F8 the following data on the concentration of C2F4 were taken. Determine the order of the reaction and the rate constant at this temperature. Assume that the reverse reaction is negligible.

Question

For the gas-phase reaction at 300°C:

[latex] C_{2}F_{4} → \frac{1}{2} cyclo-C_{4}F_{8} [/latex]

the following data on the concentration of [latex]C_{2}F_{4}[/latex] were taken. Determine the order of the reaction and the rate constant at this temperature. Assume that the reverse reaction is negligible.

Time/min	[latex]Concentration /mol L^{−1}[/latex]
0	0.0500
250	0.0250
750	0.0125
1750	0.00625
3750	0.00312

Accepted Answer

This example can be solved by inspection. Each concentration is half of the previous concentration, so that the time interval from a given data point to the next is the half-life for the reaction using the given data point as an “initial state.” We have

Half-life/min	[latex]Initial concentration/mol L^{−1}[/latex]
250	0.0500
500	0.0250
750	0.0125
1750	0.00625

The half-life doubles each time the “initial” concentration is reduced to half its previous value. This behavior indicates a second-order reaction. A linear least-squares fit of [latex]\ln (t_{1/2})[/latex] versus [latex]\ln ([A]_{0})[/latex] confirms this result with order =2.00 and [latex] k_{f}=0.080 Lmol^{−1} min^{−1}=1.3×10^{−3} Lmol^{−1} s^{−1}.[/latex]

Question 11.6: For the gas-phase reaction at 300°C: C2F4 → 1/2 cyclo-C4F8 t...

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