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To solve this question, we will use the following relation
ln [(p∞-p0) / (p∞-pt)] = kt (1)
where p∞ is the pressure of the system at infinite tim e (or very long time), p0 is the initial pressure, pt is the final pressure of the system, k is the rate constant and t is the time. Here the given equation is
A (s) ---------> 2B (g) + C (g)
As the starting material is a solid, therefore the initial pressure of the system will be zero. Hence the equation (1) will reduce to
ln [(p∞) / (p∞-pt)] = kt (2)
We are given that the pressure after a very long time is 225 mm of Hg. So p∞ =225 mm. Also pressure after 20 minutes is 150 mm, t = 20 minutes and pt = p20 = 150 mm.
Substituting the above values in equation (2), we get
ln [225 / (225 - 150)] = k X 20
this gives k = 0.05 ln 3 per minute.
So the correct answer is 0.05 ln 3 / min.
When we substitute the value of k and t = 40 in equation (1), we get
ln [225 / (225 - pt)] = 0.05 ln (3) X 40
This gives pt = 300 mm.
Regards
Arun (askIITians forum expert)
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