How would the number of moles (n) of o2 change if your atmospheric pressure was doubled and all other variables stayed the same?

The ideal gas law equation gives the relationship between pressure and number of moles 
PV = nRT
where P is pressure
V - volume
n - number of moles 
R - universal gas constant 
T - Temperature 
all the parameters remained constant therefore volume, temperature are constant 
then pressure is directly proportional to number of moles
P = kn
where k is a constant 
at the first instance 
P1 = kn ---1)
n = initial number of moles
and second instance the pressure is doubled 
then new pressure is 2P1 and lets name the new number of moles as n2
then 
2P1 = kn2 --2)
then second instance divided by the first instance 


n2 = 2n
therefore the new number of moles are twice the amount of initial number of moles 
the number of moles of O₂ have been doubled