Question

Azomethane decomposes into nitrogen and ethane at elevated temperature:
H3C–N=N–CH3 → N2 + C2H6
A chemist studying this reaction at 300°C begins an experiment with an azomethane concentration of 4.25 mM and obtains the following data:
Time(s) 100 150 200 250 300
[Azomethane] (mM) 3.29 2.90 2.55 2.25 1.98
Calculate the rate constant. Give an answer with concentration units of molarity and time units of seconds.

Answer 1

first thought: this is decomposition of azomethane, and it's first-order.

Answer 2

second thought:

for a first-order reaction:

ln(n/n0) = -k * (time difference)

so k = -ln(n/n0) / (t - t0)

n is the conc. at time t, and n0 is the conc. at an earlier time (t0)

Answer 3

oops, k is the rate constant.

Answer 4

one way to use the data is to make a y versus x plot.

the dependent variable (y-value) would be ln( conc at time t / conc at time zero)

the independent variable would be the time difference since time zero, so it's the same as time at which concentration is measured.

the data points will fall on what looks like a downward sloping straight line. the slope would be -k, so the rate constant is the negative of the slope.

Answer 5

another way is calculate the rate constant using any two data points, for example the conc. at t=0 and the conc. at t=300 seconds, then

rate constant = - ln (1.98/4.25) / (300 seconds)

so it's approx. 0.0025 second^-1

if necessary, do this for a bunch of points, then take the average.