Multiple Choice
What is the rate law for the reaction A → B if the rate constant, k, is 0.25 M⁻¹ s⁻¹ at 75 °C?
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15. Chemical Kinetics
Rate Law
Multiple Choice
What are the units for the rate constant (k) of a first-order reaction?
A
mol^{2} \, L^{-2} \, s^{-1}
B
s^{-1}
C
mol \, L^{-1} \, s^{-1}
D
L \, mol^{-1} \, s^{-1}
Verified step by step guidance1
Recall that the rate law for a first-order reaction is given by \(\text{rate} = k[A]\), where \([A]\) is the concentration of the reactant and \(k\) is the rate constant.
The rate of reaction has units of concentration per time, typically \(\text{mol} \, L^{-1} \, s^{-1}\), and the concentration \([A]\) has units of \(\text{mol} \, L^{-1}\).
To find the units of \(k\), rearrange the rate law to solve for \(k\): \(k = \frac{\text{rate}}{[A]}\).
Substitute the units into the expression: \(\text{units of } k = \frac{\text{mol} \, L^{-1} \, s^{-1}}{\text{mol} \, L^{-1}}\).
Simplify the units by canceling \(\text{mol} \, L^{-1}\), which leaves the units of \(k\) as \(s^{-1}\) for a first-order reaction.
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