The decomposition of dimethylether at 504℃ is first order with a half-life of 1570. seconds. What fraction of an initial amount of dimethylether remains after 4710. seconds?
a.1/6
b.1/8
c.1/32
d.1/16
e.1/3

The fraction of an initial amount of dimethylether that remains after 4710. seconds is 1/8.

From the information given, the decomposition of dimethylether at 504℃ is first order with a half-life of 1570 seconds.

Therefore, the fraction of an initial amount of dimethylether that remains after 4710 seconds will be:

= 1/2³

= 1/8

Therefore, the correct option is 1/8.

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1/8

Explanation:

From;

Nt/No = (1/2)^t/t1/2

N= amount of dimethylether present at time t

No= amount of diethylether present at time t=0

t= time taken for N molecules of diethylether to remain = 4710 seconds

t1/2 = half-life of diethylether = 1570 seconds

Substituting values;

Nt/No = (1/2)^4710/1570

Nt/No = (1/2)^3

Nt/No= 1/8

Hence after 4710 seconds only 1/8 molecules of dimethylether will remain