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Order of Reaction

For a certain...

Question

For a certain reaction the rate law is rate $= k [C]^{3 / 2}$ . If the rate of the reaction is $0.020$ mol L $^{- 1}$ s $^{- 1}$ when $[C]$ = $1.0$ M, what is the rate when $[C]$ = $0.60$ M?

A

0.0093

mol L

^{- 1}

s

^{- 1}

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B

0.012

mol L

^{- 1}

s

^{- 1}

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C

0.033

mol L

^{- 1}

s

^{- 1}

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D

0.040

mol L

^{- 1}

s

^{- 1}

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Solution

The correct option is A $0.0093$ mol L $^{- 1}$ s $^{- 1}$
The rate law is rate $= k [C]^{3 / 2}$
The rate of the reaction is $0.020 m o l L^{- 1} s^{- 1}$ when $[C] = 1.0$ M.
The rate law becomes $0.020 m o l L^{- 1} s^{- 1} = k [1.0 M]^{3 / 2}$
$\Rightarrow k = 0.020 m o l^{- 0.5} L^{0.5} s^{- 1}$
When, $[C] = 0.60 M$ , the rate law is
Rate $= k [C]^{3 / 2}$
Rate $= (0.020 m o l^{- 0.5} L^{0.5} s^{- 1}) \times [0.60 M]^{3 / 2}$
Rate $= 0.0093 m o l L^{- 1} s^{- 1}$

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