The isomerization of methyl isonitrile (CH₃NC) to acetonitrile (CH₃CN) was studied in the gas phase at 215°C, and the following data were obtained:
Time (s) [CH₃NC] (M)
0 0.0165
2000 0.0110
5000 0.00591
8000 0.00314
12,000 0.00137
15,000 0.00074
(a) Calculate the average rate of reaction, in M/s, for the time interval between each measurement. (c) Which is greater, the average rate between t = 2000 and t = 12,000 s, or between t = 8000 and t = 15,000 s?

Verified step by step guidance

1. To calculate the average rate of reaction for each time interval, use the formula for average rate: \( \text{Average Rate} = \frac{\Delta [CH_3NC]}{\Delta t} \), where \( \Delta [CH_3NC] \) is the change in concentration and \( \Delta t \) is the change in time.
2. For the interval between 0 and 2000 seconds, calculate \( \Delta [CH_3NC] = [CH_3NC]_{2000} - [CH_3NC]_{0} \) and \( \Delta t = 2000 - 0 \). Substitute these values into the average rate formula.
3. Repeat the calculation for each subsequent interval: 2000 to 5000 seconds, 5000 to 8000 seconds, 8000 to 12,000 seconds, and 12,000 to 15,000 seconds, using the respective concentration and time values.
4. To compare the average rates between t = 2000 and t = 12,000 seconds, and between t = 8000 and t = 15,000 seconds, calculate the average rate for each of these intervals using the same formula: \( \text{Average Rate} = \frac{\Delta [CH_3NC]}{\Delta t} \).
5. After calculating the average rates for the specified intervals, compare the values to determine which interval has the greater average rate of reaction.

Key Concepts

Reaction Rate

The reaction rate is a measure of how quickly reactants are converted into products in a chemical reaction. It is typically expressed in terms of concentration change over time, such as molarity per second (M/s). Understanding how to calculate the average rate of reaction between specific time intervals is crucial for analyzing kinetic data.

Average Rate Calculation

To calculate the average rate of a reaction over a specific time interval, one can use the formula: average rate = (change in concentration) / (change in time). This involves determining the concentration of the reactant at the beginning and end of the interval and dividing the difference by the time elapsed, allowing for a clear comparison of rates across different intervals.

Isomerization Reaction

Isomerization is a type of chemical reaction where a molecule is transformed into one of its isomers, which have the same molecular formula but different structural arrangements. In this case, methyl isonitrile is converting to acetonitrile, and understanding the nature of isomerization helps in analyzing the kinetics and mechanisms involved in the reaction.