For the reaction A(g) - 2B(g), the rate of formation of B is 6*10⁻⁴ M/s when [A] = 0.1 M, and 2.4*10⁻³ M/s when [A] = 0.4 M. Find the time (in minutes) for the concentration of A to drop from 0.6 M to 0.15 M. Use ln 2 = 0.693.

Question

For the reaction A(g) -> 2B(g), the rate of formation of B is 6*10⁻⁴ M/s when [A] = 0.1 M, and 2.4*10⁻³ M/s when [A] = 0.4 M. Find the time (in minutes) for the concentration of A to drop from 0.6 M to 0.15 M. Use ln 2 = 0.693.

Accepted Answer

20 min. Rate of disappearance of A: r = (1/2)*d[B]/dt. r1 = 3*10⁻⁴ at [A]=0.1; r2 = 1.2*10⁻³ at [A]=0.4. Ratio r2/r1 = 4 = (0.4/0.1)ⁿ => n=1 (first order). k = r/[A] = 3*10⁻⁴/0.1 = 3*10⁻³ s⁻¹. Time = (1/k)*ln(0.6/0.15) = (1/3*10⁻³)*ln4 = (2*ln2)/(3*10⁻³) = 2*0.693/0.003 = 462 s ~ 7.7 min. Hmm, let me recheck.

For the reaction A(g) -> 2B(g), the rate of formation of B is 610⁻⁴ M/s when [A] = 0.1 M, and 2.410⁻³ M/s when [A] = 0.4 M. Find the time (in minutes) for the concentration of A to drop from 0.6 M to 0.15 M. Use ln 2 = 0.693.

Solution

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