JEE Advanced 2021 Chemistry question

For the following reaction

2X + Y P

the rate of reaction is . Two moles of **X** are mixed with one mole of **Y** to make 1.0 L of solution. At 50 s, 0.5 mole of **Y** is left in the reaction mixture. The correct statement(s) about the reaction is(are) (Use: ln 2 = 0.693)

(A)The rate constant, , of the reaction is .
(B)Half-life of **X** is 50 s.Correct
(C)At 50 s, mol L s.Correct
(D)At 100 s, mol L s.Correct

Answer: (B),(C),(D)

Solution

When 0.5 mol of Y has reacted, 1.0 mol of X has reacted, so [X] falls from 2 M to 1 M in 50 s – the half-life of X is 50 s, (B) correct. Since , X decays by first-order kinetics with constant : $ = = 50 ⇒ k =

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Question ID VK-033918