Final answer:
To determine the percent dissociation at 340K, the rate constant for the decomposition of A at the new temperature must be calculated using the Arrhenius equation and then applied to the first-order rate law. A higher temperature will result in an increased rate of reaction, leading to a greater percent dissociation in a given time, all else being equal.
Step-by-step explanation:
According to the Arrhenius equation k = Ae-Ea/RT, where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. At 298K, a 20% solution of A decomposes to 25% in 20 minutes. To calculate the decomposition at 340K, we first need to determine the rate constant at the new temperature using the temperature dependence of the rate constant, and then apply the integrated rate law for a first-order reaction.
The rate of a first-order reaction is given by rate = k[A] , with the decomposition of A being directly proportional to its concentration. For a first-order reaction, the half-life is independent of the concentration of the reactant. This assumes that the decomposition of A follows first-order kinetics, which means that it depends on the concentration of A and not on the concentration of B.
Considering this, at a higher temperature of 340K, we would expect the rate of the reaction to increase due to the increased rate constant. This would lead to a greater percent dissociation in the 20-minute time period, even with a higher starting concentration of a 30% solution of A. However, to provide an exact value for the percent dissociation, one would need to perform specific calculations involving the initial concentration of A and the first-order rate law.