For the reaction $\mathrm{A} \rightarrow$ products. The concentration of A at 10 minutes is $\_\_\_\_$ $\times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1}$ (nearest integer). The reaction was started with $2.5 \mathrm{~mol} \mathrm{~L}^{-1}$ of A.

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Chemical Kinetics

For the reaction

A \to

products.

The concentration of A at 10 minutes is

____

\times 1 0^{- 3} mol L^{- 1}

(nearest integer).
The reaction was started with

2.5 mol L^{- 1}

of A.

Answer: 2435

A plot of half-life against initial concentration that is a straight line through the origin marks a zero-order reaction, for which

t_{1/2} = [A]_{0} /2 k

and the slope equals

1/2 k

. The slope of

76.92

fixes the rate constant at

k = 1/ (2 \times 76.92) = 6.5 \times 1 0^{- 3} mol L^{- 1} min^{- 1}

. For a zero-order reaction the concentration falls linearly,

[A]_{t} = [A]_{0} - k t

, so after ten minutes

[A] = 2.5 - 6.5 \times 1 0^{- 3} \times 10 = 2.435 mol L^{- 1}

, which is

2435 \times 1 0^{- 3} mol L^{- 1}

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Integer answer