In the first order, reaction A yields products, A=0.400M initially and 0.250M after 15.0 min. What is the value of the rate constant, k?

ln(No/N) kt.

No = 0.400
N = 0.250
k = ?
t = 15 min

To find the value of the rate constant (k) for the first-order reaction, we can use the integrated rate law for a first-order reaction:

ln(A(t)/A₀) = -kt

Where:
A₀ = initial concentration
A(t) = concentration at time (t)
k = rate constant
t = time

Given:
A₀ = 0.400 M
A(t) = 0.250 M
t = 15.0 min

Substituting these values into the equation, we get:

ln(0.250 M / 0.400 M) = -k * 15.0 min

Simplifying:

ln(0.625) = -k * 15.0 min

Now, we need to solve for k. To do this, we can rearrange the equation:

-k = ln(0.625) / 15.0 min

k = -ln(0.625) / 15.0 min

Using a calculator, we can find the value of k:

k ≈ 0.053 min⁻¹

So, the value of the rate constant (k) for this first-order reaction is approximately 0.053 min⁻¹.

To find the value of the rate constant (k), we can use the rate law equation for a first-order reaction:

Rate = k[A]

In this case, the initial concentration of A is 0.400M and it decreases to 0.250M after 15.0 minutes. We can use this information to calculate the rate constant (k).

First, let's calculate the initial rate (R1) using the initial concentration of A:

R1 = k[A]1

Here, [A]1 is the initial concentration of A. In this case, [A]1 = 0.400M.

Next, let's calculate the rate at 15.0 minutes (R2) using the final concentration of A:

R2 = k[A]2

Here, [A]2 is the final concentration of A. In this case, [A]2 = 0.250M.

Since the rate is given by the change in concentration over time, we can calculate the average rate (Ravg) using the following equation:

Ravg = (R2 - R1) / (t2 - t1)

Here, t1 is the initial time and t2 is the final time. In this case, t1 = 0 min and t2 = 15.0 min.

Now, let's substitute the values into the equation to find the average rate:

Ravg = (R2 - R1) / (t2 - t1)
Ravg = (0.250M - 0.400M) / (15.0 min - 0 min)
Ravg = -0.150M / 15.0 min
Ravg = -0.010M/min

Now, we have the average rate (-0.010M/min) and the initial concentration of A (0.400M). We can use these values to calculate the value of the rate constant (k).

Ravg = k[A]1

-0.010M/min = k * 0.400M

Now, let's solve for k:

k = -0.010M/min / 0.400M
k = -0.025 min^-1

Therefore, the value of the rate constant (k) is -0.025 min^-1.

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