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JEE Main levelOne or more correct optionsDifficulty 2 of 3ck131

For a first-order reaction $A (g) B (g) + C (g)$ in a rigid vessel starting with pure A at $P_{0}$ , which statements are correct? ( $P_{t}$ is the total pressure at time $t$ .)

AThe partial pressure of A is $2 P_{0} - P_{t}$
B $P_{\infty} = 2 P_{0}$
C $P_{t} - P_{0}$ equals the pressure of A that has reacted
D $k = \frac{1}{t} ln \frac{P _{0}}{P _{t} - P _{0}}$

Answer: A, B, C

Each mole of A gives 2 mol of gas so

P_{\infty} = 2 P_{0}

, and

P_{t} = P_{0} + x

gives

x = P_{t} - P_{0}

and

p_{A} = P_{0} - x = 2 P_{0} - P_{t}

. The correct log form is

ln [P_{0} / (2 P_{0} - P_{t})]

, not

ln [P_{0} / (P_{t} - P_{0})]

, so the third statement is wrong.

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