Question 14.4.4: Use the integrated rate law to calculate time for percent re......
Use the integrated rate law to calculate time for percent reacted.
The isomerization of methyl isonitrile to acetonitrile in the gas phase at 250 ºC is first order (k = 3.00 × 10^{-3} s^-1).
CH_{3}NC(g) → CH_{3}CN(g)
How much time is required for 90.0% of the CH_{3}NC initially present in a reaction flask to be converted to product at 250 ºC?
You are asked to calculate the amount of time required for a given percentage of a reactant to be converted to product.
You are given the balanced equation for the reaction, the order of the reaction with respect to the reactant, the rate constant for the reaction, and the percentage of reactant to be converted to product.
Use the first-order integrated rate equation and the fact that if 90.0% of the methyl isonitrile is consumed, only 10.0% remains in the flask.
ln\frac{\left[CH_{3}CN\right]_{t} }{\left[CH_{3}CN\right]_{0}} = -kt
\frac{\left[CH_{3}CN\right]_{t} }{\left[CH_{3}CN\right]_{0}} = \frac{10.0}{100.0} = 0.100
k = 3.00 × 10^{-3} s^{-1}
ln(0.100) = −(3.00 × 10^{-3} s^{-1})t
t = 768 seconds