What are the units of the rate constant k in the following rate law? rate = k [X]^0 [Y]^0

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

Answer: (C)

Verified step by step guidance

1. Identify the given rate law: \(\text{rate} = k [X]^0 [Y]^0\). Since any concentration raised to the zero power is 1, this simplifies to \(\text{rate} = k\).
2. Recognize that the rate of a reaction is generally expressed in units of concentration per time, typically \(\mathrm{mol\ L^{-1}\ s^{-1}}\).
3. Since \([X]^0\) and \([Y]^0\) are both 1, the rate law reduces to \(\text{rate} = k\), meaning the rate constant \(k\) must have the same units as the rate itself to keep the equation dimensionally consistent.
4. Therefore, the units of \(k\) are the same as the units of the rate, which are \(\mathrm{s^{-1}}\) in this case because the rate is independent of concentration (zero order).
5. Conclude that for a zero-order reaction, the rate constant \(k\) has units of \(\mathrm{mol\ L^{-1}\ s^{-1}}\), but since the rate law here shows no concentration dependence, the rate constant units simplify to \(\mathrm{s^{-1}}\).