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Question

The decomposition of an aqueous solution of ammonium nitrite was studied. The volume of nitrogen gas collected at different intervals of time was follows:
Time(minutes)101520Vol. of N2(mL)6.259.0011.4035.05
From the above data prove that the reaction is of the first order.

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Solution

For this reaction:
K=1tlnVVVt;V=35.05
Values of K at different times are:-
Time VVt 1tlnVVVt=k
10 min 35.05-6.25=28.80
110ln35.0528.80=0.019min1
15 min 35.05-9.00=26.05 115ln35.0526.05=0.019min1
20 min 35.05-11.40=23.65 120ln35.0523.65=0.019min1
25 min 35.05-13.65=21.40 125ln35.0521.40=0.019min1
As value of K is constant it shows that it is first order reaction.

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