Chapter 3: Rate Laws

Rate Laws

What is the reaction rate law for the reaction if the reaction is elementary? What is r_B? What is r_C?  Calculate the rates of A, B, and C in a CSTR where the concentrations are C_A = 1.5 mol/dm³, C_B = 9 mol/dm³ and k_A = 2 (dm³/mol)^(1/2)(1/s).

Hint 1: What is r_A?

Hint 2: What is r_B?

Hint 3: What is r_C?

Full Solution

Back to Problem

\(-r_A = k_A C_A C_B^{1/2}\)

\(\frac{r_B}{1/2} = \frac{r_A}{1}\)

\(r_B = \frac{r_A}{2}\)

\(r_B = -\left(\frac{k_A}{2}\right)C_A C_B^{1/2}\)

Back to Problem

\(\frac{r_C}{1} = \frac{r_A}{(-1)}\)

\(r_C = -r_A = k_A C_A C_B^{1/2}\)

\(r_C = k_A C_A C_B^{1/2}\)

Back to Problem

What is the reaction rate law for the reaction \(A + \frac{1}{2}B \rightarrow C\) if the reaction is elementary? What is r_B? What is r_C?  Calculate the rates of A, B, and C in a CSTR where the concentrations are C_A = 1.5 mol/dm³, C_B = 9 mol/dm³ and k_A = 2 (dm³/mol)^(1/2)(1/s).

Solution

\(-r_A = k_A C_A C_B^{1/2}\)

\(\frac{r_B}{(1/2)} = \frac{r_A}{1}\)

\(r_B = \frac{r_A}{2}\)

\(r_B = -\left(\frac{k_A}{2}\right)C_A C_B^{1/2}\)

\(\frac{r_C}{1} = \frac{r_A}{(-1)}\)

\(r_C = -r_A = k_A C_A C_B^{1/2}\)

Let's calculate the rate if,

\(k_A = 2 \left(\frac{\text{dm}^3}{\text{mol}}\right)^{1/2} \frac{1}{\text{s}}\)

\(C_A = 1.5 \frac{\text{mol}}{\text{dm}^3}\)

\(C_B = 9 \frac{\text{mol}}{\text{dm}^3}\)

Then

\(-r_A = \left( 2 \left( \frac{\text{dm}^3}{\text{mol}} \right)^{1/2} \frac{1}{\text{s}} \right) \left( 1.5 \frac{\text{mol}}{\text{dm}^3} \right) \left( 9 \frac{\text{mol}}{\text{dm}^3} \right)^{1/2}\)

\(-r_A = 9 \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}}\)

\(r_B = \frac{1}{2} \left(-k_A C_A C_B^{1/2}\right)\)

\(r_B = -4.5 \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}}\)

\(r_C = -r_A\)

\(r_C = 9 \frac{\text{mol}}{\text{dm}^3 \cdot \text{s}}\)