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Grade: 12
        The reaction A(s)- 2B(g) + C(g) is first order . The pressure after 20 min. And after very long time are 150 mm Hg and 225 mm Hg . The value of rate constant and pressure after 40 min. are
2 years ago

Answers : (1)

Arun
23755 Points
							
Dear Amit
 

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)

2 years ago
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