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

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117
Jun 9, 2016

The units for $k$ are ${\text{s}}^{- 1}$, ${\text{L·mol"^(-1)"s}}^{- 1}$, and ${\text{L"^2"mol"^(-2)"s}}^{- 1}$.

Explanation:

The units come from the rate laws

rate = $k {\left[\text{A}\right]}^{n}$, where $n$ is the order of the reaction. So

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

$n$ = 1: $k = {\text{rate"/(["A"]) = ("mol·L"^-1"s"^-1)/("mol·L"^-1) = "s}}^{-} 1$

$n$ = 2: $k = {\text{rate"/(["A"]^2) = ("mol·L"^-1"s"^-1)/(("mol·L"^-1)^2) = "L·mol"⁻¹"s}}^{-} 1$

$n$ = 3: $k = {\text{rate"/(["A"]^3) = ("mol·L"^-1"s"^-1)/("mol·L"^-1)^3 = "L"^2"mol"^-2"s}}^{-} 1$

In summary,

$k = {\text{rate"/(["A"]^n) = ("mol·L"^-1"s"^-1)/(("mol·L"^-1)^n) = "L"^(n-1)"mol"^(1-n)"s}}^{-} 1$

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