Question

Calculate the density of air(as a perfect gas) when the pressure

is1.01325*105 N/m2 and the temperature
is288.15 K.

Answer 1

1.2253 kg/m3

Step-by-step explanation:

from ideal gas equation we know that

`PV = n*RT`

`(n)/(V) = (P)/((RT))`

where,

pressure P = 1.01325 x 10^5 N/m2 = 101325 Pascals

gas constant R = 8.314 J/mol/K

T = 288.15 K

`(n)/(V) = (101325)/((8.314*288.15K))`

`(n)/(V) = 42.2948967 Pa*mol/J`

we know that 1 Pa = 1 J/m3

so
`(n)/(V) = 42.2948967\  mol/m3`

as we know, Air consist of 21% oxygen and 79% nitrogen

therefore

Molar mass of air:

`0.21 *(32 g/mol) + 0.79 *(28 g/mol) = 28.97 g/mol`

So
`(42.2948967\  mol/m3) * 28.97\  g/mol`

= 1 225.27 g/m^3

= 1.22528316 kg/m^3 ~ 1.2253 kg/m3