Chemical Kinetics and Nuclear ChemistryHard

Question

The decomposition reaction 3A(g) → 2B(g) + 2C(s) follows first-order kinetics. Starting with pure ‘A’ (at 6 atm), the pressures of system after 20 minutes and after a very long time are 5.05 atm and 4.05 atm, respectively. Identify the correct statement(s) related with the reaction.

Options

A.Time for 75% completion of reaction is slightly more than 40 minutes.
B.Time for 87.5% completion of reaction is slightly less than 60 minutes.
C.Time for 93.75% completion of reaction is exactly 80 minutes.
D.The pressure of system after 40 minutes will be 4.55 atm.

Solution

3A(g) ? 2B(g) + 2C(s)

t = 0 6 atm 0 –

t = 20 min (6 – x) atm 2/3 x atm 0.05 atm

t = ∞ ≈ 0 4 atm 0.05 atm

But from question, P∞ = 4.05 atm and hence, (4.05 – 4) = 0.05 atm is the vapour pressure of C(s).

Now, $P_{20} = (6 - x) + \frac{2}{3}x + 0.05 = 5.05 \Rightarrow x = 2$

∴ t =20 min = t1/2

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