To calculate the concentration of N2O5 after 315.0 minutes have passed, we can use the first-order rate equation:

ln(N2O5t)N2O5=−kt

Where:

- N2O5t is the concentration of N2O5 at time t
- N2O5 is the initial concentration of N2O5
- k is the rate constant
- t is the time

Rearranging the equation, we have:

N2O5t=N2O5×e−kt

Given:

- N2O5=0.393M
- k=0.00410min−1
- t=315.0min

Substituting these values into the equation:

N2O5t=0.393e−0.00410315.0

Calculating this expression:

N2O5t=0.162M

**Explanation:**

Therefore, the concentration of N2O5 after 315.0 minutes have passed is approximately 0.162 M.

### Step 3 of 3

Now, let’s calculate the concentration of (CH2)3 after s seconds have passed using a similar approach.

The first-order rate equation for the rearrangement of cyclopropane to propene is:

ln((CH2)3t)/(CH2)3)=−kt

Where:

- (CH2)3t is the concentration of (CH2)3 at time t
- (CH2)3 is the initial concentration of (CH2)3
- k is the rate constant
- t is the time

Rearranging the equation, we have:

(CH2)3t=(CH2)3×e−kt

Given:

- (CH2)3 = 0.126 M
- k=0.000670s−1
- (CH2)3t=0.0296M

Substituting these values into the equation:

0.0296=0.126e−0.000670s

Solving for s:

s=−ln(0.0296/0.126)/0.000670

Calculating this expression:

s=6,545sec

**Explanation:**

using the first-order approach we can find the seconds.

##### Final solution

Therefore, the concentration of (CH2)3 will be 0.0296 M after 6,545 sec have passed.