PCl5( g) decomposes at temperature T K in to PCl3( g) and Cl2( g) according to 1st order kinetics. In a closed container initially only PCl5(g ) was taken at 2atm & T K. After 12 seconds the pressure in container found to be 2.4 atm at same temperature. The rate constant (in min-1) for the decomposition of PCl5(g ) at T K is
Question
PCl5( g) decomposes at temperature T K in to PCl3( g) and Cl2( g) according to 1st order kinetics. In a closed container initially only PCl5(g ) was taken at 2atm & T K. After 12 seconds the pressure in container found to be 2.4 atm at same temperature. The rate constant (in min-1) for the decomposition of PCl5(g ) at T K is
Solution
The reaction is given as:
PCl5(g) → PCl3(g) + Cl2(g)
This is a first order reaction, so we can use the first order rate equation:
k = 1/t * ln([A]0/[A])
where: k is the rate constant, t is the time, [A]0 is the initial concentration (or in this case, pressure) of PCl5, [A] is the concentration (or pressure) of PCl5 at time t.
Given: [A]0 = 2 atm (initial pressure of PCl5), [A] = 2.4 atm - 2 atm = 0.4 atm (pressure of PCl5 after 12 seconds), t = 12 seconds = 0.2 minutes (converted from seconds to minutes).
Substituting these values into the rate equation:
k = 1/0.2 min * ln(2 atm/0.4 atm) k = 5 min^-1 * ln(5) k = 5 min^-1 * 1.60944 k = 8.0472 min^-1
So, the rate constant for the decomposition of PCl5(g) at T K is approximately 8.05 min^-1.
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