Question

A perfect gas sample contains 6.2*^22 molecules per cubic meter at 205 k. calculate the pressure of this gas and express the answer in units of pascals, bar, atm, and mmHg.

Answer 1

mole of gas = 6.2 * 10^22 / 6.023 * 10^23 = 0.1029 mole.

V = 1 m^3 = 1000 L

T = 205 K

ideal gas equation is

PV = nRT

P = nRT / V = 0.1029 * 0.0821 * 205 / 1000 = 1.73 * 10^-3 atm

thus

pressure in atm = 1.73 * 10^-3 atm

and

pressure in mm Hg = 1.73 * 10^-3 * 760 = 1.32 mm Hg

and

pressure in pascal =  1.73 * 10^-3 * 101325 = 175.3 pascals

and

pressure in bar =  1.73 * 10^-3 * 1.01 = 1.75 * 10^-3 bar