Final answer:
The rate constant is given for the rearrangement of methyl isonitrile to acetonitrile. The molarity of CH₃NC after 2.00 hours, the time for the concentration to drop to 0.0300 M, and the time for 20% of CH₃NC to react can be calculated using the first-order rate equation.
Step-by-step explanation:
The rate of the rearrangement of methyl isonitrile 1CH₃NC₂ to acetonitrile 1CH₃CN₂ is a first-order reaction. The rate constant is given as 5.11 × 10⁻⁵ s⁻¹ at 472 K. To answer the questions:
(a) To find the molarity of CH₃NC after 2.00 hours, we can use the first-order rate equation:
[CH₃NC]t = [CH₃NC]₀ * e^(-kt)
where [CH₃NC]t is the concentration at time t, [CH₃NC]₀ is the initial concentration, k is the rate constant, and t is the time elapsed. Plugging in the values, we get:
[CH₃NC]₂h = 0.0340 * e^(-5.11 × 10⁻⁵ * 2.00 * 3600)
(b) To find the time required for the CH₃NC concentration to drop to 0.0300 M, we can rearrange the first-order rate equation:
t = (-1/k) * ln([CH₃NC]t/[CH₃NC]₀)
Plugging in the values, we get:
t = (-1/5.11 × 10⁻⁵) * ln(0.0300/0.0340)
(c) To find the time required for 20% of CH₃NC to react, we can use the same first-order rate equation:
t = (-1/k) * ln([CH₃NC]t/[CH₃NC]₀)
Plugging in the values, we get:
t = (-1/5.11 × 10⁻⁵) * ln(0.80)