Given info:
Reaction: 3A+2B--->2C+D
{A] (mol/L)
1.0 ×10^-2
1.0 ×10^−2
2.0 ×10^−2
2.0 ×10^−2
3.0 ×10^−2
[B] (mol/L)
1.0
3.0
3.0
1.0
3.0
Rate of appearance of C (mol/L-hr)
0.30×10^−6
8.10×10^−6
3.24×10^−5
1.20×10^−6
7.30×10^−5
Calculate the specific rate constant?
To calculate the specific rate constant for the given reaction, we can use the rate equation:
rate = k[A]^m[B]^n
where:
rate is the rate of the reaction,
[A] and [B] are the concentrations of reactants A and B, respectively,
k is the specific rate constant, and
m and n are the orders of reactants A and B, respectively.
From the given reaction, we can determine the order of reactants A and B by using the stoichiometric coefficients. The order of reactant A is the exponent to which [A] is raised in the rate equation, and similarly for reactant B.
Looking at the balanced reaction:
3A + 2B ---> 2C + D
We see that the stoichiometric coefficient of A is 3, and the stoichiometric coefficient of B is 2. Therefore, the reaction is first-order with respect to A (m = 1) and first-order with respect to B (n = 1).
Now we can use the rates of appearance of C and the concentrations of A and B to calculate the specific rate constant.
Let's take one set of data from the given information:
[A] = 1.0 × 10^-2 mol/L
[B] = 1.0 mol/L
rate = 0.30 × 10^-6 mol/L-hr
Plugging these values into the rate equation, we get:
0.30 × 10^-6 = k * (1.0 × 10^-2)^1 * (1.0)^1
Simplifying the equation, we have:
0.30 × 10^-6 = k * 1.0 × 10^-2
Dividing both sides of the equation by 1.0 × 10^-2, we get:
k = (0.30 × 10^-6) / (1.0 × 10^-2)
Calculating this expression, we find:
k = 3.0 × 10^-5
Therefore, the specific rate constant for the given reaction is 3.0 × 10^-5 (mol/L-hr)^-1.