### Test for First Order Reaction

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 504oC 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

```
1. Test for a first order reaction.
2. Calculate the value of the specific reaction rate at 504oC

Calculations:

Total pressure of the system (p) and partial pressure of A (pA)are related as:

pA = pAo - (a/Dn)(p - po)

where, po is the initial pressure of the system;

pAo 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, po = pAo = 312 mm Hg (Assuming feed is pure A)

a = 1

Dn = 3-1 = 2

pA = 312 - (1/2)(p - 312)

i.e.,

pA = 312 - 0.5 (p - 312)

pA for various times are calculated as follows:

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

pA (mm Hg) 264 224 187 78.5 2.5

Fractional conversion of A is given by:

XA = (pAo - pA) / pAo

For various time values, XA and -ln(1- XA) is calculated and tabulated as follows:

`Time (Sec)		390	777	1195	3155	a`

pA (mm Hg) 264 224 187 78.5 2.5

XA 0.154 0.282 0.401 0.748 0.992

-ln(1 - XA) 0.167 0.331 0.512 1.378 4.828

For a first order reaction, a plot of t Vs. -ln(1 - XA) 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. HOME