What are the units for k in first, second, and third order reactions?

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Answer:

The units for #k# are #"s"^(-1)#, #"L·mol"^(-1)"s"^(-1)#, and #"L"^2"mol"^(-2)"s"^(-1)#.

Explanation:

The units come from the rate laws

rate = #k["A"]^n#, where #n# is the order of the reaction. So

#k = "rate"/["A"]^n = (("mol·L"^-1)"s"^-1)/(("mol·L"^-1)^n) #

#n# = 1: #k = "rate"/(["A"]) = ("mol·L"^-1"s"^-1)/("mol·L"^-1) = "s"^-1#

#n# = 2: #k = "rate"/(["A"]^2) = ("mol·L"^-1"s"^-1)/(("mol·L"^-1)^2) = "L·mol"⁻¹"s"^-1#

#n# = 3: #k = "rate"/(["A"]^3) = ("mol·L"^-1"s"^-1)/("mol·L"^-1)^3 = "L"^2"mol"^-2"s"^-1#

In summary,

#k = "rate"/(["A"]^n) = ("mol·L"^-1"s"^-1)/(("mol·L"^-1)^n) = "L"^(n-1)"mol"^(1-n)"s"^-1#

The video below also shows you how to determine the units of the rate constant.

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