The decomposition of XY is second-order in XY and has a rate constant of 0.00895 M-1s-1 at a certain temperature. If the initial concentration of XY is 0.194 M, how long (in seconds) will it take for the concentration to decrease to 0.047 M?

Why did XY go to therapy? Because it needed to decompose its problems!

In this case, we can use the integrated rate law for a second-order reaction, which is:

1/[XY]t - 1/[XY]0 = kt

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

Let's plug in the values we know:

1/0.047 - 1/0.194 = 0.00895t

To solve for t, we can rearrange the equation:

1/0.047 - 1/0.194 = 0.00895t

(1/0.047 - 1/0.194)/0.00895 = t

Calculating that gives us t ≈ 87.3 seconds.

So, it will take approximately 87.3 seconds for the concentration of XY to decrease to 0.047 M.

To determine the time it takes for the concentration of XY to decrease from 0.194 M to 0.047 M, we can use the integrated rate law for a second-order reaction:

1/[XY]t - 1/[XY]0 = kt

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

Rearranging the equation, we have:

t = (1/[XY]t - 1/[XY]0) / k

Given:
Initial concentration, [XY]0 = 0.194 M
Final concentration, [XY]t = 0.047 M
Rate constant, k = 0.00895 M^-1s^-1

Plugging in the values into the equation, we get:

t = (1/0.047 - 1/0.194) / 0.00895

Calculating this expression yields:

t = (21.2766 - 5.1546) / 0.00895

t = 16.122 / 0.00895

t ≈ 1802.79 seconds

Therefore, it will take approximately 1802.79 seconds for the concentration of XY to decrease from 0.194 M to 0.047 M.

To find the time it takes for the concentration of XY to decrease to 0.047 M, we can use the integrated rate law for a second-order reaction:

1/[XY]t - 1/[XY]0 = kt

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

To rearrange the equation to solve for time, we can rewrite it as:

1/[XY]t = kt + 1/[XY]0

Now, let's plug in the given values:

[XY]t = 0.047 M
[XY]0 = 0.194 M
k = 0.00895 M^(-1)s^(-1)

1/0.047 M = (0.00895 M^(-1)s^(-1))t + 1/0.194 M

To simplify further, we can subtract 1/0.194 M from both sides:

1/0.047 M - 1/0.194 M = (0.00895 M^(-1)s^(-1))t

Multiplying the denominators:

(0.194 - 0.047)/(0.047 * 0.194) = (0.00895 M^(-1)s^(-1))t

Simplifying the equation:

0.147/0.009118 = t

t = 16.13 s (rounded to two decimal places)

Therefore, it will take approximately 16.13 seconds for the concentration of XY to decrease to 0.047 M.