Question

Decomposition of X yields Y and Z. Use following data:

Time, min	[X], M	Time, min	[X], M
0	0.86	40	0.274
10	0.635	50	0.207
20	0.484	60	0.146
30	0.365

If after 30 minutes, the concentrations of Y and Z were 0.190M and 0.310M determine the rate constants for their formation.

Answer 1

To determine the rate constant for the formation of product we first calculate the order of decomposition of X by plotting the graph between concentration of X versus time and ln[X] versus time.

From the above plots we see that conc. of X decreases exponentially with time and also ln[X] versus time is a straight line. Hence the decomposition of X is a first order reaction.

Rate constant for the formation of X and Y will be same as rate constant for decomposition of X.

Rate constant for decomposition of X can be determined from the integrated rate law as:

k = 1/t ln [X₀]/[X_t]

For t= 30 min, k = 1/30 ln 0.86/0.365 = 0.0286 min^-1