What are the units of the rate constant k in the rate law: rate = k[x][y]?

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

Answer: (C)

Verified step by step guidance

1. Identify the rate law given: \(\text{rate} = k [x][y]\). Here, the rate depends on the concentration of two reactants, each raised to the first power, so the overall reaction order is 2 (first order in \(x\) and first order in \(y\)).
2. Recall that the rate of a reaction has units of concentration per time, typically \(\mathrm{mol \\ L^{-1} \\ s^{-1}}\).
3. Concentrations \([x]\) and \([y]\) each have units of \(\mathrm{mol \\ L^{-1}}\). Since the rate law is \(k [x][y]\), the units of \(k\) must balance the units so that the product \(k [x][y]\) has units of \(\mathrm{mol \\ L^{-1} \\ s^{-1}}\).
4. Set up the units equation: \([k] \times (\mathrm{mol \\ L^{-1}}) \times (\mathrm{mol \\ L^{-1}}) = \mathrm{mol \\ L^{-1} \\ s^{-1}}\).
5. Solve for the units of \(k\): \([k] = \frac{\mathrm{mol \\ L^{-1} \\ s^{-1}}}{(\mathrm{mol \\ L^{-1}})^2} = \mathrm{mol^{-1} \\ L \\ s^{-1}}\).