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Oxyacids of Phosphorus

The rate cons...

Question

The rate constant for the IInd order neutralization of 2-nitropropane by aqueous alkali obeys the equation.
$l o g_{10} K = \frac{3163}{T} + 12$ , T is temperature in Kelvin.
Time and concentration were in minute and mol $l i t r e^{- 1}$ respectively. The half-life at ${43.3}^{o} C$ and for an initial concentration of 0.001 mol $l i t r e^{- 1}$ for each of the reactant in minutes is $10^{- x} m i n$ ,then value of $x$ is_________.

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Solution

$T = 43.3 + 273 K = 316.3 K$
$l o g_{10} K = \frac{3163}{T} + 12 = \frac{3163}{316.3} + 12 = 10 + 12 = 22$
$K = 10^{22}$
$t_{1 / 2} = \frac{1}{k a} = \frac{1}{10^{22} \times 0.001} = 10^{- 19} m i n$

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