Question

A reaction was observed for 15 days and the percentage of
the reactant remaining after the days indicated was recorded
in the following table :
Time(days 0 2 4 6 8 10 12 14 15

% reactant
remaining 100 50 39 25 21 18 15 12.5 10

Which one of the following best describes the order and the
half-life of the reaction?
Reaction Order Half-life (days)
(a) First 2
(b) First 6
(c) Second 2
(d) Zero 6

Answer 1

Answer:

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Answer 2

half life of reaction is 2 days & order of reaction is 2

option (c) is correct

Time(days) 0 2 4 6 8 10 12 14 15

% reactant

remaining 100 50 39 25 21 18 15

12.5 10

• half life : Time taken by reaction for concentration of reactants to become half

• It is clear from observation that

half life is 2 days as % of remaining

reactant after two days is 50%.

• Now,let the order of reaction is n

• For nth order reaction

• K = 1/t(n-1)[1/(a-x)^n-1 + 1/(a)^n-1]

where x is conc. of reactant consumed

• a is initial concentration of

reactant

• For , t = 2 days x = a/2

• K = 1/2(n-1)[1/(a-a/2)^n-1 + 1/(a)^n-1]

• K = 1/2(n-1)[ {(2^n-1) -1}/(a)^n-1]__(1)

• For , t = 6 days x = 3a/4

• K = 1/2(n-1)[1/(a-3a/4)^n-1 + 1/(a)^n-1]

• K = 1/2(n-1)[ {(4^n-1) -1}/(a)^n-1]__(2)

• Dividing 1 &2

• 1 = 1/2{(2^n-1) -1}/(1/6){(4^n-1) -1}

• Using a²-b² = (a-b)(a+b)

• 1 = 3{(2^n-1)-1}/{(2^n-1)-1}{(2^n-1)+1}

• 1 = 3/ {(2^n-1)+1}

By cross multiplying

• {(2^n-1)+1} = 3

• (2^n-1) = 2

• (2^n-1) = 2¹

• on comparing

• n-1 =1

• n =2

• order of reaction is 2.