a concentration-time study of the gas phase reaction a 2A3 -> 3A2 produced the data in the table below.

time [A3] (M) [A2] (M)
0 4.00 *10^-4 0
10 2.00 *10^-4 3.00 *10^-4
20 1.00 *10^-4 4.50 *10^-4
10 5.00 *10^-5 ?

A) What is the concentration of A2 in the time interval 20-30 seconds?
I got 7.50 x 10^-6

B) What is the concentration of A2 after 30 seconds?

I'm confused on how to do both problems please help

To determine the concentration of A2 in the time interval of 20-30 seconds, we can first calculate the rate of change of A2 concentration using the data given.

Step 1: Calculate the rate of change of A2 concentration between 10-20 seconds.
Rate = ([A2]final - [A2]initial) / (time final - time initial)
Rate = (4.50 * 10^-4 M - 3.00 * 10^-4 M) / (20 s - 10 s)
Rate = 1.50 * 10^-4 M / 10 s
Rate = 1.50 * 10^-5 M/s

Note: We are assuming that the reaction is a first-order reaction since the concentration of A2 is changing linearly with time.

Step 2: Extrapolate the rate of change of A2 concentration to find the concentration at 30 seconds.
Rate = (concentration at 30 seconds - concentration at 20 seconds) / (30 s - 20 s)
1.50 * 10^-5 M/s = (concentration at 30 s - 4.50 * 10^-4 M) / 10 s
concentration at 30 s = (1.50 * 10^-5 M/s * 10 s) + 4.50 * 10^-4 M
concentration at 30 s = 1.50 * 10^-4 M + 4.50 * 10^-4 M
concentration at 30 s = 6.00 * 10^-4 M

Therefore, the concentration of A2 in the time interval 20-30 seconds is 6.00 * 10^-4 M.

Now, to determine the concentration of A2 after 30 seconds, we can use the result obtained above.

Step 3: Calculate the rate of change of A2 concentration after 30 seconds.
Rate = ([A2]final - [A2]30 s) / (time final - 30 s)
Rate = (concentration after 30 s - 6.00 * 10^-4 M) / (10 s)
Rate = (? - 6.00 * 10^-4 M) / 10 s
Rate = 1.50 * 10^-5 M/s (Note: This is the same as the rate calculated earlier.)

Step 4: Extrapolate the rate of change of A2 concentration to find the concentration after 40 seconds.
1.50 * 10^-5 M/s = (? - 6.00 * 10^-4 M) / 10 s
? = (1.50 * 10^-5 M/s * 10 s) + 6.00 * 10^-4 M
? = 1.50 * 10^-4 M + 6.00 * 10^-4 M
? = 7.50 * 10^-4 M

Therefore, the concentration of A2 after 30 seconds is 7.50 * 10^-4 M.

To solve both problems, we need to analyze the given concentration-time data and determine the trends in the concentrations of A3 and A2. Let's break down each problem step by step:

A) What is the concentration of A2 in the time interval 20-30 seconds?

To find the concentration of A2 in the time interval 20-30 seconds, we need to examine the change in concentration of A2 during this time period. We can observe that the concentration of A2 increases from 4.50 * 10^-4 M at t = 20 seconds to an unknown value at t = 30 seconds.

To determine the change in concentration of A2, we can subtract the concentration at t = 20 seconds from the concentration at t = 30 seconds. However, the concentration at t = 30 seconds is not given.

To estimate the concentration at t = 30 seconds, we can look at the trend in the data. From t = 0 to t = 10 seconds, we see that the concentration of A2 increases by 3.00 * 10^-4 M. Therefore, it is reasonable to assume that the same increase in concentration occurs in the next 10 seconds (t = 10 to t = 20 seconds).

Thus, we can estimate that the concentration of A2 at t = 30 seconds is (4.50 * 10^-4 M) + (3.00 * 10^-4 M) = 7.50 * 10^-4 M.

Now, we can subtract the concentration at t = 20 seconds (4.50 * 10^-4 M) from the estimated concentration at t = 30 seconds (7.50 * 10^-4 M):

Concentration of A2 in the time interval 20-30 seconds = (7.50 * 10^-4 M) - (4.50 * 10^-4 M) = 3.00 * 10^-4 M

So, the concentration of A2 in the time interval 20-30 seconds is 3.00 * 10^-4 M.

B) What is the concentration of A2 after 30 seconds?

To find the concentration of A2 after 30 seconds, we need to consider the trend in the change of concentration throughout the given data.

From t = 0 to t = 10 seconds, we observe that the concentration of A2 increases by 3.00 * 10^-4 M. From t = 10 to t = 20 seconds, it increases by 1.50 * 10^-4 M. Assuming the same rate of increase continues, we can estimate the concentration of A2 at t = 30 seconds by adding the previous rate of increase (1.50 * 10^-4 M) to the concentration at t = 20 seconds (4.50 * 10^-4 M):

Estimated concentration of A2 at t = 30 seconds = (4.50 * 10^-4 M) + (1.50 * 10^-4 M) = 6.00 * 10^-4 M

Therefore, the concentration of A2 after 30 seconds is 6.00 * 10^-4 M.

Remember, these estimates are based on an assumption of a consistent rate of change between the given data points. They provide a reasonable approximation, but actual experimental data would be needed for a more accurate answer.

Time (s) [A3] (M) [A2] (M)

0 4.00 × 10–4 0
10 2.00 × 10–4 3.00 × 10–4
20 1.00 × 10–4 4.50 × 10–4
30 5.00 × 10–5