The first-order reaction, SO2Cl2 �¨ SO2 + Cl2, has a rate constant equal to 2.20 �~ 10-5 s-1 at 593 K. What percentage of the initial amount of SO2Cl2 will remain after 6.00 hours?

62.2%

To determine the percentage of the initial amount of SO2Cl2 that will remain after 6.00 hours, we can use the first-order reaction rate equation:

ln(A/A0) = -kt

Where:
A = amount of SO2Cl2 remaining at time t
A0 = initial amount of SO2Cl2
k = rate constant
t = time

We need to rearrange the equation to solve for A/A0:

ln(A/A0) = -kt
A/A0 = e^(-kt)

Now we can substitute the given values and solve for A/A0:

k = 2.20 x 10^(-5) s^(-1) (rate constant)
t = 6.00 hours = 6.00 x 60 x 60 = 21,600 seconds (convert hours to seconds)

A/A0 = e^(-kt)
A/A0 = e^(-2.20 x 10^(-5) s^(-1) * 21,600 s)

Calculating the exponent:

-2.20 x 10^(-5) s^(-1) * 21,600 s = -0.4752

A/A0 = e^(-0.4752)

Using a calculator, e^(-0.4752) is approximately 0.6227.

Therefore, approximately 62.27% of the initial amount of SO2Cl2 will remain after 6.00 hours.

To find the percentage of the initial amount of SO2Cl2 that will remain after 6.00 hours, we can use the first-order reaction equation:

ln([A]/[A0]) = -kt

where [A] is the concentration of SO2Cl2 at a given time, [A0] is the initial concentration of SO2Cl2, k is the rate constant, and t is the time.

First, let's rearrange the equation to solve for [A] (concentration at a given time):

[A] = [A0] * e^(-kt)

Next, we need to calculate the concentration of SO2Cl2 after 6.00 hours using the rate constant given. We can convert the time into seconds:

Time = 6.00 hours * 60 minutes/hour * 60 seconds/minute
= 21600 seconds

Now, plug in the values into the equation:

[A] = [A0] * e^(-kt)
[A] = [A0] * e^(-2.20 * 10^-5 s^-1 * 21600 s)

To find the percentage of the initial amount of SO2Cl2 that will remain after 6.00 hours, we need to divide the concentration at 6.00 hours by the initial concentration ([A0]), and then multiply by 100 to get the percentage:

Percentage remaining = ([A] / [A0]) * 100

Now, let's calculate it step by step:

1. Calculate [A]:

[A] = [A0] * e^(-2.20 * 10^-5 s^-1 * 21600 s)

2. Calculate the percentage remaining:

Percentage remaining = ([A] / [A0]) * 100

By plugging in the values into the equations, you should be able to find the answer.