The gas phase decomposition of A takes place according to the irreversible reaction, A à 3P. The kinetics of the reaction was studied by measuring the increase in pressure in a constant volume reaction vessel. At 504^{o}C and an initial pressure of 312 mm Hg, the following data were obtained:

Time (Sec) 390 777 1195 3155 a Total pressure (mm Hg) 408 488 562 779 931

- Test for a first order reaction.
- Calculate the value of the specific reaction rate at
504
^{o}C

Calculations:

Total pressure of the system (p) and partial pressure of A (p_{A})are related as:

p_{A} = p_{Ao} - (a/Dn)(p - p_{o})

where, p_{o} is the initial pressure of the system;

p_{Ao} is the initial pressure of A;

a is the stoichiometric coefficient of A;

and Dn = stoichiometric coefficient of products minus reactants.

For the given problem, p_{o} = p_{Ao} = 312 mm Hg (Assuming feed is pure A)

a = 1

Dn = 3-1 = 2

p_{A} = 312 - (1/2)(p - 312)

i.e.,

p_{A} = 312 - 0.5 (p - 312)

p_{A} for various times are calculated as follows:

Time (Sec) 390 777 1195 3155 a Total pressure (mm Hg) 408 488 562 779 931

p_{A} (mm Hg) 264 224 187 78.5 2.5

Fractional conversion of A is given by:

X_{A} = (p_{Ao} - p_{A}) / p_{Ao }

For various time values, X_{A} and -ln(1- X_{A}) is calculated and tabulated as follows:

Time (Sec) 390 777 1195 3155 a

p_{A} (mm Hg) 264 224 187 78.5 2.5

X_{A} 0.154 0.282 0.401 0.748 0.992

-ln(1 - X_{A}) 0.167 0.331 0.512 1.378 4.828

For a first order reaction, a plot of t Vs. -ln(1 - X_{A}) in a linear XY graph is a straight line with a slope of k.

From the following plot, it is seen that the given data is for a first order reaction.