A first-order reaction takes 69.3 min for 50% completion. What is the time needed for 80% of the reaction to get completed?

Question 1:.A first-order reaction takes 69.3 min for 50% completion. What is the time needed for 80% of the reaction to get completed?

The correct answer is -The time required for a reaction to reach a certain extent of completion can be determined using the half-life (t1/2) of the reaction, which is the time taken for half of the reactants to be consumed. The half-life of a first-order reaction is constant and can be calculated using the rate constant (k) of the reaction.

The relationship between half-life and the extent of completion (x) can be expressed as:

t1/2 = 0.693/k

Where k = -ln(1/2)/t1/2

We can use this relationship to find the time required for 80% completion as follows:

First, we need to find k.

k = -ln(1/2)/t1/2 = -ln(1/2)/(69.3/2)

Next, we need to find the half-life of the reaction when 80% of the reactants have been consumed.

Let’s call the time required for 80% completion t80. Then, the extent of completion after t80 would be 0.8 * 0.5 = 0.4.

Using the relationship between half-life and extent of completion:

t80/2 = 0.693/k = 0.693/-ln(0.4)/k

Next, we can solve for t80:

t80 = 2 * t80/2 = 2 * 0.693/-ln(0.4)/k

We can now use the logarithmic values given in the question to find t80:

t80 = 2 * 0.693/-ln(0.4)/k = 2 * 0.693/(0.3010 – log(0.4)) = 2 * 0.693/(0.3010 – 0.5228)

t80 = 2 * 0.693/(-0.2218) = 2 * 0.693/0.2218

t80 = 6.48 min

Therefore, it would take 6.48 minutes for 80% of the reaction to get completed.