Question

At 300 K, the half life of a sample of a gaseous compound initially at 1 atm is 100 sec. When the initial pressure at same temperature is 0.5 atm the half life is 50 sec, the order of the reaction is x. What is the value of x?

Answer 1

Half life of zero order reaction is directly proportional to initial concentration,
$t_{\frac{1}{2}}=\frac{[A{]}_0}{2K}$
Here, instead of concentration we are dealing with pressure, at constant temperature partial pressure and concentration of gas are directly related as:
$P=CRT$
So, as initial pressure is reduced to half of its value, $t_{1/2}$ will also reduced to half as given in question.
The answer would be zero here.