Rate constant of a first order reaction:
The rate constant (k) is a proportionality constant that relates the rate of a chemical reaction to the concentration of reactants. In the case of a first order reaction, the rate of the reaction is directly proportional to the concentration of the reactant.

Given information:
Rate constant (k) = 0.0693 per minute

Calculating the percentage of constant remaining:
To calculate the percentage of the constant remaining at the end of 60 minutes, we need to use the first-order reaction equation:

ln([A]t/[A]0) = -kt

Where [A]t is the concentration of the reactant at time t, [A]0 is the initial concentration of the reactant, k is the rate constant, and t is the time.

At the end of 60 minutes, t = 60 minutes. We can rearrange the equation to solve for [A]t:

[A]t = [A]0 * e^(-kt)

Substituting the given values:

[A]t = [A]0 * e^(-0.0693 * 60)

Now we can calculate the percentage of the constant remaining:

Percentage remaining = ([A]t / [A]0) * 100

Substituting the values of [A]t and [A]0:

Percentage remaining = ([A]0 * e^(-0.0693 * 60) / [A]0) * 100

Simplifying the equation:

Percentage remaining = e^(-0.0693 * 60) * 100

Using a scientific calculator:

Percentage remaining ≈ 50.07%

Explanation:
The percentage of the constant remaining at the end of 60 minutes for a first order reaction with a rate constant of 0.0693 per minute is approximately 50.07%. This means that only half of the initial concentration of the reactant remains after 60 minutes. The rate constant determines the rate at which the reactant concentration decreases over time. In this case, the rate constant indicates that the reaction is relatively slow, as only half of the reactant is consumed after 60 minutes.