Question

Consider the decomposition of acetaldehyde (CH₃CHO) into methane (CH₄) and carbon monoxide (CO).

CH₃CHO → CH₄ + CO

An experiment is performed where the concentration of acetaldehyde is measured at various time intervals, resulting in the following data.

Time (s)	[CH3CHO] (M)
0.0	0.242
20.0	0.168
40.0	0.129
60.0	0.104

(a) Using Excel (or similar software), graph the three types of plots outlined below and enter the slope, y-intercept, and R² for each graph). Use the graph with the best linear fit to determine the order of the reaction with respect to CH₃CHO. (Enter your answer to three significant figures.)

graph (1):    [CH₃CHO]_tvs. time

slope	=
y-intercept	=
R2	=

graph (2):    ln [CH₃CHO]_t vs. time

slope	=
y-intercept	=
R2	=

graph (3):    1/[CH₃CHO]_tvs. time

slope	=
y-intercept	=
R2	=

Recall that for a  ---Select--- zero order first order second order reaction, a plot of [CH₃CHO] vs. time will yield a straight line. For a  ---Select--- zero order first order second order reaction, a plot of ln[CH₃CHO] vs. time will yield a straight line. For a  ---Select--- zero order first order second order reaction, a plot of 1/[CH₃CHO] vs. time will yield a straight line. The graph of 1/[CH₃CHO] vs. time has the best fit to a straight line, so this reaction is  ---Select--- zero order first order second order .

(b) Calculate the rate constant for this reaction.
1/M·s

(c) Determine the rate law for this reaction. (Rate expressions take the general form: rate = k . [A]^a . [B]^b.)

Answer 1

(a) Graph 1:

[CH3CHO] vs. time

equation: y= -0.0023x + 0.223

slope	= -0.0023
y-intercept	= 0.2283
R2	= 0.9428

Graph 2:

ln[CH3CHO] vs. time

Equation: y= -0.014x - 1.4588

slope	=  -0.014
y-intercept	= 1.4588
R2	= 0.9856

Graph 3:

1/[CH3CHO] vs. time

Equation: y= 0.0912x + 4.1256

slope	=  0.0912
y-intercept	= 4.1256
R2	= 0.9999 = 1

From the above plot, for a second order reaction, a plot of 1/[CH3CHO] vs time will yield a straight line. The graph of 1/[CH3CHO] vs. time has the best fit to a straight line, so this reaction is second order. .
(b)The rate constant for this reaction.1/M·s

For a second order reaction the slope of 1/[CH3CHO] vs time gives the rate constant. Since the slope of the plot is  0.0912. The rate constant = 0.0912.1/M·s

(c) The rate law for this reaction.

The rate law for second order reaction can be expressed as below