For a reaction A → B, if the rate constant k is 0.1 s^-1, what is the time requi
Practice Questions
Q1
For a reaction A → B, if the rate constant k is 0.1 s^-1, what is the time required for the concentration of A to decrease to 25% of its initial value?
10 seconds
20 seconds
30 seconds
40 seconds
Questions & Step-by-Step Solutions
For a reaction A → B, if the rate constant k is 0.1 s^-1, what is the time required for the concentration of A to decrease to 25% of its initial value?
Step 1: Identify the type of reaction. This is a first-order reaction because it follows the form A → B.
Step 2: Write down the formula for the time required in a first-order reaction: t = (ln(2)/k) * ln([A]0/[A]t).
Step 3: Determine the initial concentration [A]0. This is 100% of A.
Step 4: Determine the final concentration [A]t. Since we want to find the time when A decreases to 25%, [A]t is 25% of [A]0.
Step 5: Convert percentages to a fraction. 25% is 0.25, so [A]t = 0.25 * [A]0.
Step 6: Substitute the values into the formula. We have k = 0.1 s^-1, [A]0 = 1 (for simplicity), and [A]t = 0.25.
Step 7: Calculate the natural logarithm of 2: ln(2) ≈ 0.693.
Step 9: Substitute these values into the formula: t = (0.693 / 0.1) * 1.386.
Step 10: Calculate the time: t = 6.93 * 1.386 ≈ 9.63 seconds.
Step 11: Since we want the time for A to decrease to 25%, we can also use the simplified version: t = (ln(2)/0.1) * ln(4) = 20 seconds.
First-Order Kinetics – The question tests understanding of first-order reaction kinetics, specifically how to calculate the time required for a reactant's concentration to decrease to a certain percentage of its initial value using the rate constant.
Natural Logarithm in Kinetics – It assesses the ability to apply natural logarithms in the context of chemical kinetics, particularly in the formula relating concentration and time.
