Question

The table gives the concentrations of C2H4O(g)C2H4O(g) as a function of time at a certain temperature for the reaction shown.C2H4O(g)⟶CH4(g)+CO(g)C2H4O(g)⟶CH4(g)+CO(g)Verify that this is a first-order reaction by plotting ln[C2H4O]ln[C2H4O] versus time and determining the value of the rate constant.[C2H4O] (M) Time (min)0.0860 0.000.0465 58.00.0355 83.00.0274 107.00.0174 150.0

Answer 1

To verify a first-order reaction, ln[C2H4O] versus time is plotted, seeking a linear relationship. The slope of this line, calculated using two points, provides the rate constant (-k) for the reaction.

Step-by-step explanation:

To determine whether the reaction C2H4O(g) → CH4(g) + CO(g) is first-order, we can plot the natural logarithm (ln) of the concentration of C2H4O over time and look for a linear relationship. If the plot of ln[C2H4O] versus time is a straight line, this suggests that the reaction is first-order, as per the first-order rate law which states that rate = k[C2H4O], where k is the rate constant. The slope of this line would then give us the value of the negative rate constant (-k).

To calculate the rate constant, we would take two points on the straight line of the graph and use the formula:

k = (ln[C2H4O]_initial - ln[C2H4O]_final) / (t_final - t_initial)

Using the given concentration and time data, we would calculate the ln[C2H4O] for each concentration, plot these values against the time, and then determine the slope of the resulting line.