How many moles of oxygen are present in a `550 cm^3` sample of a gas at a pressure of 1.5 atm and at a temperature of `27^@C`? (Given, R = 8.31 k Pa `dm^3 K^(-1) mol^(-1)`).

Explanation

Since the value of R is given in k Pa `dm^3 K^(-1) mol^(-1)` (SI unit), the units of pressure and volume must correspond to it i.e., pressure should be expressed in k Pa and volume in `dm^3`. Therefore,
`P= 1.5 atm = 1.5 xx 101.325 = 152 k Pa " " ( :. 1 atm = 101.325 k Pa)`
`V = 550 cm^3 = 550 xx 10^(-3) dm^3 = 0.550 dm^3 ( :. 1 cm^3 = 10^(-3) dm^3)`
`T = 27^@C = 273 + 27 = 300 K " and " n` = ?
According to the ideal gas equation,
PV = nRT
or `n= (PV)/(RT)=( 152 xx 0.550)/( 8.31 xx 300) =3.35xx10^(-2)` moles.