Chapter 12, Problem 42E

At 500 K in the presence of a copper surface, ethanol decomposes according to the equation

${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}\left(g\right)\to {\text{CH}}_3\text{CHO}\left(g\right)+{\text{H}}_2\left(g\right)$

The pressure of C₂H₅OH was measured as a function of time and the following data were obtained:

Time(s)	$P_{{\text{C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}}\left(\text{torr}\right)$
0	250.
100.	237
200.	224
300.	211
400.	198
500.	185

Since the pressure of a gas is directly proportional to the concentration of gas, we can express the rate law for a gaseous reaction in terms of partial pressures. Using the above data, deduce the rate law, the integrated rate law, and the value of the rate constant, all in terms of pressure units in atm and time in seconds. Predict the pressure of C₂H₅OH after 900. s from the start of the reaction. (Hint: To determine the order of the reaction with respect to C₂H₅OH, compare how the pressure of C₂H₅OH decreases with each time listing.)