Question

Chemical x decomposes via the reaction below. The reaction is a first order reaction and has an activation energy of 45.000 kJ mol⁻¹. The half-life of chemical x at 25 °C is 4.90 min. If the reaction below is performed at a temperature of 40 °C beginning with a 1.00 m concentration of x, how long until only 0.100 m of x is left? assume the reverse reaction is negligible.

Answer 1

To determine the time it takes for Chemical X to decrease from 1.00 M to 0.100 M at 40 °C in a first-order reaction, calculate the rate constant at 25 °C using the given half-life, then use the Arrhenius equation to find the rate constant at 40 °C, and apply the first-order kinetics formula.

Step-by-step explanation:

The student has presented a scenario involving a chemical reaction where Chemical X decomposes in a first order reaction with a known activation energy and half-life at a certain temperature. The task is to determine how long it will take for the concentration of Chemical X to decrease from 1.00 M to 0.100 M at an increased temperature of 40 °C. To solve this, we can use the Arrhenius equation to find the new rate constant at 40 °C and then apply the first-order kinetics formula to find the time required for this concentration change.

The half-life of a first-order reaction is related to the rate constant (k) by the formula t1/2 = 0.693 / k. This relationship allows us to calculate k at 25 °C using the given half-life of 4.90 minutes. Once k at 25 °C is found, we can calculate the rate constant at 40 °C using the Arrhenius equation and the provided activation energy. With the new k value at 40 °C, we can find the time needed for the reaction to decrease the concentration of Chemical X to 0.100 M using the formula ln([X0]/[X]) = kt, where [X0] is the initial concentration and [X] is the final concentration.