calculate the specific rate constant
A] (mol/L) [B] (mol/L) Rate of appearance of C (mol/L-hr)
1.0 ×10^-2 1.0 0.30×10^−6
1.0 ×10^−2 3.0 8.10×10^−6
2.0 ×10^−2 3.0 3.24×10^−5
2.0 ×10^−2 1.0 1.20×10^−6
3.0 ×10^−2 3.0 7.30×10^−5
To calculate the specific rate constant, we can use the rate of appearance of C and the concentrations of reactants A and B. The specific rate constant can be determined by using the rate equation for the reaction:
Rate = k * [A]^m * [B]^n
Where k is the specific rate constant, [A] and [B] are the concentrations of reactant A and B respectively, and m and n are the stoichiometric coefficients of reactants A and B in the balanced chemical equation.
From the given data, we have the concentrations of A and B, and the rate of appearance of C. We can choose any set of concentrations of A and B along with the corresponding rate of appearance of C, and substitute these values into the rate equation to solve for k.
Let's choose the second set of concentrations:
[A] = 1.0 × 10^-2 mol/L
[B] = 3.0 mol/L
Rate of appearance of C = 8.10 × 10^-6 mol/L-hr
Substituting these values into the rate equation:
8.10 × 10^-6 mol/L-hr = k * (1.0 × 10^-2 mol/L)^m * (3.0 mol/L)^n
To solve for k, we need another set of concentrations and the corresponding rate of appearance of C. Let's choose the fourth set of concentrations:
[A] = 2.0 × 10^-2 mol/L
[B] = 1.0 mol/L
Rate of appearance of C = 1.20 × 10^-6 mol/L-hr
Substituting these values into the rate equation:
1.20 × 10^-6 mol/L-hr = k * (2.0 × 10^-2 mol/L)^m * (1.0 mol/L)^n
Now, we have two equations with two unknowns (m and n) and two sets of concentrations and rates of appearance of C. We can solve these equations simultaneously to find the values of m and n.
After determining the values of m and n, we can substitute these values along with any set of concentrations and the corresponding rate of appearance of C into the rate equation to solve for the specific rate constant (k).