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How many moles of gas and how many molecules of O2 are in the cylinder

A certain German sports car engine has a cylinder volume of 618cm^3. The cylinder is full of air at 75 C and 802 mm Hg. How many moles of gas in the cylinder? If air is 20.0% O2 by volume, how many molecules of oxygen are present?

My method involves the knowledge that 1 mole of a gas occupies 22.4 L at stp. So using (p1v1)/t1 = (p2v2)/t2 allows a missing value to be found. Let v2 = 618 cm3, p2= 802mm, t2 = 348K (273+75) while v1 is the volume at stp, p1 = 760mm and t1 = 273K.
So calculate the volume that the gas in the cylinder would occupy at stp. Then find the number of moles of gas that this represents since 1 mole occupies 22.4L. (The number of moles of gas will be the same at stp as at the conditions of the experiment).
Then find 20% of this to represent the number of moles of Oxygen present.
Then use Avogadro constant (6.02 x 1023) to find the number of molecules present (1 mole of O2 will contain 6.02 x 1023 molecules.

Perhaps you are taught to use PV=nRT.