What are the units of the rate constant k in the rate law: rate = k[x]^2[y]^2, where rate is in mol L^{-1} s^{-1} and concentrations are in mol L^{-1}?

• A. L^3 mol^{-3} s^{-1}
• B. mol L^{-1} s^{-1}
• C. s^{-1}
• D. L^2 mol^{-2} s^{-1}

Answer: (A)

Verified step by step guidance

1. Identify the overall order of the reaction by summing the exponents of the concentration terms in the rate law. Here, the rate law is rate = k[x]^2[y]^2, so the order is 2 + 2 = 4.
2. Recall the general form of the rate law: rate = k [A]^m [B]^n ..., where the units of rate are typically mol L^{-1} s^{-1} and the units of concentration are mol L^{-1}.
3. Write the units of the rate and the concentrations explicitly: rate has units mol L^{-1} s^{-1}, and each concentration term [x] and [y] has units mol L^{-1}. Since both are squared, their combined units are (mol L^{-1})^2 * (mol L^{-1})^2 = (mol L^{-1})^{4}.
4. Set up the equation for the units of k by rearranging the rate law units: units of k = (units of rate) / (units of concentration)^{order} = (mol L^{-1} s^{-1}) / (mol L^{-1})^{4}.
5. Simplify the units expression by dividing: (mol L^{-1} s^{-1}) / (mol^{4} L^{-4}) = mol^{1 - 4} L^{-1 + 4} s^{-1} = mol^{-3} L^{3} s^{-1}. Therefore, the units of k are L^{3} mol^{-3} s^{-1}.