SN2 - What is the result of increasing solvent volume by 2. Does rate decrease b

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I'm looking at my notes from Chad's Gen. Chem. videos and I wrote for an SN2 reaction where Rate = k [Nucleophile][Electrophile] that if the solvent volume increases by 2, the rate decrease by 1/16. Should the rate decrease by 1/4 not 1/16?

 

[bluesolic]

I'm looking at my notes from Chad's Gen. Chem. videos and I wrote for an SN2 reaction where Rate = k [Nucleophile][Electrophile] that if the solvent volume increases by 2, the rate decrease by 1/16. Should the rate decrease by 1/4 not 1/16?

the rate is decreased by 1/4, because if solvent is doubled, the the [ nuc ] and [ elec ] is decreased by 1/2 and that's 1/4 for the rate..

I don't know where you saw 1/16, but 1/4 is correct answer.