Question

The conversion of methyl isonitrile to acetonitrile in the gas phase at 250 °C CH3CN(g) is first order in CH3NC with a rate constant of 3.00×10^-3 s-1. If the initial concentration of CH3NC is 5.45×10^-2 M, the concentration of CH3NC will be 1.56×10^-2 M after_____________ s have passed.

Answer 1

Answer: The concentration of $CH_3NC$ will be $1.56\times 10^{-2}M$ after 416 seconds have passed.

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant = $3.00\times 10^{-3}s^{-1}$

t = age of sample = ?

a = let initial amount of the reactant = $5.45\times 10^{-2}M$

a - x = amount left after decay process = $1.56\times 10^{-2}M$

$t=\frac{2.303}{3.00\times 10^{-3}}\log\frac{5.45\times 10^{-2}}{1.56\times 10^{-2}}$

$t=416s$

The concentration of $CH_3NC$ will be $1.56\times 10^{-2}M$ after 416 seconds have passed.