Question

A certain first-order reaction is 35.5 percent complete in 4.90 min at \(25^{\circ} \mathrm{C}\). What is its rate constant?

Short answer

The rate constant (k) is obtained by solving the equation with the given values, which is generally in the units of 1/s for first-order reactions. Remember to change the time to seconds for meaningful comparison and standard analysis in chemistry.

Step-by-step solution

Identifying given values

First, identify the known values from the given problem. Here, it is given that the reaction is 35.5 percent complete, which in fraction amounts to 0.355 (X = 0.355). The time it takes for the reaction to reach this point is 4.90 minutes (t = 4.90).

Converting time to appropriate unit

It is generally accepted to have the rate constant k in units of 1/s for first-order reactions. So, convert the given time from minutes to seconds. That is, \( t = 4.90 \times 60 = 294 \) seconds.

Solving for rate constant (k)

Substitute these values back into the equation \( k = \frac{-\ln(1-X)}{t} \). You will get \( k = \frac{-\ln(1-0.355)}{294} \). Solving the above equation will yield a numerical value for k.