Let the gaseous reaction be :-

A----> B
Now,

The rate of the first-order gaseous reaction can be written as:
r = k[A] {k = rate constant}

Now,

The general unit of rate constant k is given as = {(mol / L)^(1-n)} / (time)

Where, n = order of reaction
And time can be in sec, min, hour, etc.

So unit of rate constant k for 1st order ( n = 1 ) gaseous reaction is : 1 / (time)

Now, for gaseous reactions, the concentrations are measured in terms of partial pressure .

So, [A] will have the unit of pressure. Now, taking the unit of pressure as atm we will proceed you can take any other unit of pressure also, but we will proceed with general pressure unit i.e atm.

Therefore, the unit of rate (r) will be : atm / time

Where, (time can be in sec, min, hour, etc.)

[ Note : 1atm = 101325 Pascals ]
[ Note : Pascal is SI unit of Pressure ]