Experiment 1: A has .20 M, B has .20 M and the initial rate is 2.0*10^-4M/min

Experiment 2: A has .20 M, B has .40 M, and the initial rate is 8.0*10^-4M/min
Experiment 3: A has .40 M, B has .40 M, and the initial rate is 1.6*10^-3M/min

Using the data above, answer the following questions:

Determine the rate law for the reaction

Calculate the value of the specific rate constant

If the initial concentrations of both A and B are .3 M at what initial rate is C formed?

For the first question I got (a)(b)^2, but the other 2 I have no clue on how to find those out.

Your rate = k(A)(B)^2 is correct(that's #1).

For #2 plug rate for any ONE of the trials, plug (A) and (B) for that trial and solve for k.

#3. You now know k, plug in 0.3 and 0.3 and solve for rate but I would feel better if I saw an equation for the reaction of A and B to produce C.

Its A + 2B --> C

So for 2 would I do (a)(b)^2=Rate and plug in the numbers for the correspond letters from whichever trial I choose?

yes.

#2 is like this.
8E-4 = k*(0.2)(0.4)^2 and solve for k or
2E-4 = k*(0.2)(0.2)^2 and solve for k or
1.6E-3 = k*(0.4)(0.4)^2. Note that all of them give the same value for k.
For #3, the rate of disappearance of A = rate of appearance of C since the coefficient of each = 1.

So if I used 8E-4 = k*(0.2)(0.4)^2

My answer would be .025 M/min
Then from there I would do .025(.30)(.3)^2 which would be 6.75E-4 right?

That's what I would do.

To determine the rate law for the reaction, we need to analyze how the initial rate (r) changes with respect to the initial concentrations of reactants A and B.

Experiment 1: A has 0.20 M, B has 0.20 M, and the initial rate is 2.0 * 10^-4 M/min.
Experiment 2: A has 0.20 M, B has 0.40 M, and the initial rate is 8.0 * 10^-4 M/min.
Experiment 3: A has 0.40 M, B has 0.40 M, and the initial rate is 1.6 * 10^-3 M/min.

Comparing experiments 1 and 2, we can see that doubling the initial concentration of B results in a fourfold increase in the initial rate. This indicates that the rate is directly proportional to the square of the concentration of B (i.e., rate ∝ [B]^2).

Now, comparing experiments 2 and 3, we can see that doubling the initial concentration of both A and B results in a fourfold increase in the initial rate. This indicates that the rate is directly proportional to the concentration of A (i.e., rate ∝ [A]).

Combining these findings, we can deduce the rate law for the reaction:

Rate = k[A][B]^2

To calculate the value of the specific rate constant (k), we need to select any of the experiments and substitute the given values into the rate law equation. Let's choose experiment 1:

2.0 * 10^-4 M/min = k * (0.20 M) * (0.20 M)^2
2.0 * 10^-4 M/min = k * 0.008 M^3
k ≈ (2.0 * 10^-4 M/min) / (0.008 M^3)
k ≈ 0.025 M^-2 min^-1

Hence, the value of the specific rate constant k is approximately 0.025 M^-2 min^-1.

To find the initial rate at which product C is formed when both A and B have an initial concentration of 0.3 M, we can use the rate law equation. Let's call the initial rate as "r_initial" and substitute the given concentrations:

r_initial = k * (0.3 M) * (0.3 M)^2
r_initial = k * 0.027 M^3

Now, substitute the previously calculated value of k into the equation:

r_initial = (0.025 M^-2 min^-1) * 0.027 M^3

Simplifying the equation will give you the value of the initial rate at which product C is formed.