What is the unit of the rate constant for a second-order reaction?

What is the unit of the rate constant for a second-order reaction?

Correct Answer: L²/mol²·s

Step 1: Understand that a second-order reaction means the rate of the reaction depends on the concentration of two reactants or the square of the concentration of one reactant.
Step 2: Recall the general formula for the rate of a reaction: Rate = k [A]^n, where k is the rate constant and [A] is the concentration of the reactant.
Step 3: For a second-order reaction, n = 2, so the formula becomes: Rate = k [A]^2.
Step 4: The unit of rate (change in concentration over time) is typically mol/L·s (moles per liter per second).
Step 5: The unit of concentration [A] is mol/L (moles per liter).
Step 6: Substitute the units into the rate equation: Rate = k [A]^2 becomes (mol/L·s) = k (mol/L)².
Step 7: Rearranging gives k = (mol/L·s) / (mol/L)².
Step 8: Simplifying this gives k = (mol/L·s) * (L²/mol²) = L²/mol²·s.
Step 9: Therefore, the unit of the rate constant for a second-order reaction is L²/mol²·s.

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