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JEE Main 2023 · Chemistry · Chemical Kinetics · hard

The gaseous reaction A(g)→2B(g)+C(g) is first order in A. Starting with pure A at 100 torr in a rigid vessel at constant temperature, the total…

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The gaseous reaction A(g)→2B(g)+C(g)\mathrm{A(g)\to2B(g)+C(g)} is first order in A. Starting with pure A at 100100 torr in a rigid vessel at constant temperature, the total pressure is 250250 torr after 1010 minutes. The total pressure (in torr) after 1515 minutes is
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Answer: 275

If pp is the partial pressure of A that has reacted, total pressure =100−p+2p+p=100+2p=100-p+2p+p=100+2p. At 1010 min, 250=100+2p250=100+2p, so p=75p=75, leaving 2525 torr of A: that is 100→25100\to25, two half-lives, so t1/2=5t_{1/2}=5 min. At 1515 min (three half-lives) A left =12.5=12.5 torr, p=87.5p=87.5, total pressure =100+2(87.5)=275=100+2(87.5)=275 torr.
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