Solve Kinetics Question: Zero Order Reaction at High Pressure

[mooncrater]

Homework Statement

The question says:
The decomposition of a gas on a surface follows the rate law : Rate is proportional to $\frac {kP}{1+kP}$, where $P$ is the pressure and $k$ is a constant. Find the order of the reaction at high pressure.

Homework Equations

The Attempt at a Solution

In the solution they have said that since $P$ is high therefore $kP>>>1$ due to which rate is proportional to $\frac {kP}{kP}=1$ which means the rate is a constant so it is a zero order reaction. What I say is that since they don't known the value of $k$ how can they come to the conclusion that $kP>>>1$? If we assume k to be equal to a very very small number such that $1>>>kP$ then their assumption fails, and the rate is not a constant.
So am I right about this thing or making a mistake?

 

[Chestermiller]

If doesn't matter what the value of k is. If you take a high enough pressure, the order will approach zero.

chet

 

[mooncrater]

If doesn't matter what the value of k is. If you take a high enough pressure, the order will approach zero.

chet

But if we leave that proven part (I. e if pressure is increased order will tend towards zero) and use only this :
Rate is proportional to $$\frac {kP}{1+kP} $$
Then isn't the value of $k$ important?

 

[Chestermiller]

But if we leave that proven part (I. e if pressure is increased order will tend towards zero) and use only this :
Rate is proportional to $$\frac {kP}{1+kP} $$
Then isn't the value of $k$ important?

Sure. At pressures less than on the order of 1/k.

Chet