Problem 34 - General Chemistry: Principles and Modern Applications

Question

A reaction is \(50 \%\) complete in 30.0 min. How long after its start will the reaction be \(75 \%\) complete if it is (a) first order; (b) zero order?

Step-by-Step Solution

Answer

The time after the start at which the reaction will be 75% complete is approximately 44.7 minutes for a first order reaction and approximately 45.0 minutes for a zero order reaction.

Step 1: Analyze the given problem

The exercise provides that the reaction is 50% complete in 30.0 minutes and it is required to calculate the time required for the reaction to be 75% complete for a first order and zero order reaction. The amount of the reaction completed is given by \(N = 1 - e^{-kt}\). For a first order reaction, this simplifies to \( t = t_{1⁄2}*\log_2 (1/(1-N)) \). For a zero order reaction, we have \( N = kt \)

Step 2: Calculate time for a first order reaction

Using given values and first order rate law we have: \( t = (30min)*\log_2(1/(1-0.75)) \). Evaluating this yields approximately 44.7 minutes.

Step 3: Calculate time for a zero order reaction

For zero order reaction, the formula becomes \( N = kt \). Solving for k from existing data we get \( k = N/t = 0.50/30min \). Substituting this k into the equation for N=0.75 we find \( t = N/k = 0.75/(0.50/30min) \). Evaluating this gives approximately 45.0 minutes.