Establish the kinetics of the thermal decomposition of Nitrous oxide from the following data and find the reaction rate at 990^{o}C and an initial pressure of 200 mm Hg.

t, min 20 53 100 % decomposition 23 50 73

Calculations:

Conversion (X_{A})of Nitrous oxide (A) for various time values are given are given.

We shall test the date for first order, second order kinetics by integral method of analysis.

For a first order reaction, -ln(1 - X_{A}) vs. t is a straight line.

t, min 20 53 100 X_{A}0.23 0.50 0.73

t, min |
20 |
53 |
100 |

XA |
0.23 |
0.5 |
0.73 |

1-XA |
0.77 |
0.5 |
0.27 |

-LN(1 - XA) |
0.261365 |
0.693147 |
1.309333 |

From the above data the following graph is drawn:

For a second order reaction,

X_{A}/(C_{Ao} (1- X_{A}) ) = kt

i.e., X_{A}/(1 - X_{A}) vs. t is a straight line

t, min |
20 |
53 |
100 |

XA/(1 - XA) |
0.298701 |
1 |
2.703704 |

From the above data the following graph is drawn:

By comparing the two graphs, it can be seen that **First order kinetics** is well fiiting the given data.
Fisrt order rate constant k is obtained from the slope of the first order data graph, and it is = 0.0131 sec^{-1}.

Therefore, -r_{A} = kC_{A} = kC_{Ao}(1 - X_{A}) = kp_{Ao}(1 - X_{A})/RT = (1 - X_{A}) x 0.0131 x (200/760) x 101325 /(8314 x (990 + 273)) = 3.327 x 10^{-5}(1 - X_{A})

i.e., **-r _{A} = 3.327 x 10^{-5}(1 - X_{A})**

where X_{A} is fractional decomposition of Nitrous oxide, and
-r_{A} is the rate of decomposition of Nitrous oxide.