Problem 4-38 (a) Treatment of t e r t -butyl alcohol with concentrated HCl gives

Question

Problem 4-38 (a)

Treatment of tert-butyl alcohol with concentrated HCl gives tert-butyl chloride.
When the concentration of H+ is doubled, the reaction rate doubles. When the concentration of tert-butyl alcohol is tripled, the reaction rate triples. When the chloride ion concentration is quadrupled, however, the reaction rate is unchanged.

Part A

Choose the right rate equation for this reaction.

Thanks. It would help if you can explain the answer to me so I can understand this.

a. rate = k [(CH3)3CCl ] [ H2O] b. rate = k [(CH3)3COH ]2[Cl-] c. rate = k [(CH3)3COH ] [ H+ ] d. rate = k [(CH3)3COH ] [ H+ ][Cl-] e. rate = k [(CH3)3COH ] 2[ H+ ]3[Cl-]4 f. rate = k [(CH3)3CCl ]

Explanation / Answer

Solution :-

When the concentration of H+ is doubled, the reaction rate doubles.

Lets assume initial concentration is 1 then final concentration after doubling is 2

Assume initial rate is 1 so after doubling the concentration rate doubles so the final rate is 2

So we can find the order with respect to H+ as

Rate 2/ rate 1 = ([H+]2/[H+]1)^m

2/1 = [2/1]^m

2 = 2^m

Log 2 = m *log 2

m = log 2 / log 2

m= 1

therefore order with H+ is first order

When the concentration of tert-butyl alcohol is tripled, the reaction rate triples.

Lets assume initial concentration is 1 then final concentration after tripling is 3

Assume initial rate is 1 so after doubling the concentration rate tripled so the final rate is 3

Rate 2/ rate 1 = ([tert-butyl alcohol]2/[ tert-butyl alcohol]1)^n

3/1 = [3/1]^n

3 = 3^n

Log 3 = n *log 3

n = log 3 / log 3

n= 1

So the order of the tert-butyl alcohol is first order

When the chloride ion concentration is quadrupled, however, the reaction rate is unchanged.

This means reaction is zero order with the Cl-

Therefore the correct rate law equation for the reaction is option c that is

rate = k [(CH3)3COH ] [ H+ ]

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