To calculate the rate of this chemical reaction, you'll use the given rate law:
[tex]\[ \text{Rate} = k[A]^3[B]^2 \][/tex]
Here, [tex]\( k \)[/tex] is the rate constant, [tex]\( [A] \)[/tex] is the concentration of reactant A in moles per liter (M), and [tex]\( [B] \)[/tex] is the concentration of reactant B in moles per liter (M).
Given that [tex]\( k = 0.01 \)[/tex], [tex]\( [A] = 2 \ \text{M} \)[/tex], and [tex]\( [B] = 3 \ \text{M} \)[/tex], we can now plug these values into the rate law:
[tex]\[ \text{Rate} = 0.01 \cdot (2)^3 \cdot (3)^2 \][/tex]
Next, we calculate the concentrations raised to their respective powers:
[tex]\([A]^3 = 2^3 = 2 \cdot 2 \cdot 2 = 8\)[/tex]
[tex]\([B]^2 = 3^2 = 3 \cdot 3 = 9\)[/tex]
Now we multiply these numbers with the rate constant:
[tex]\[ \text{Rate} = 0.01 \cdot 8 \cdot 9 \][/tex]
[tex]\[ \text{Rate} = 0.01 \cdot 72 \][/tex]
Multiplying [tex]\( 0.01 \)[/tex] by [tex]\( 72 \)[/tex] gives us:
[tex]\[ \text{Rate} = 0.72 \][/tex]
So, the rate of the reaction is [tex]\( 0.72 \)[/tex] mole per liter per second ([tex]\(\text{M/s}\)[/tex]).
