Question

A gaseous compound Y contains carbon and hydrogen only and has a density

of 1.696 g dm-3 at 95.3 kPa pressure and 298K. Assume that Y behaves ideally,
calculate its molar mass and deduce its molecular formula. Given 1kPa =1 x 103Nm-2

.

Answer 1

`M=44.06(g)/(mol)`

Step-by-step explanation:

Hello.

In this case, knowing the temperature, density and temperature of Y which behaves ideally, we can write the ideal gas equation:

`PV=nRT`

Whereas the moles are equal to the mass over the molar mass of Y:

`PV=(m)/(M) RT`

Thus, solving for the molar mass we write:

`M=(mRT)/(PV)`

Yet, since density is mass of over volume, we then write:

`M=(\rho RT)/(P)`

Considering the pressure in atm and the density in g/L:

`P=95.3kPa*(1atm)/(101.325kPa)=0.941atm\\\\\rho=1.696(g)/(dm^3) *(1dm^3)/(1L)=1.696(g)/(L)`

Therefore, by plugging the values in, we obtain:

`M=(1.696(g)/(L) *0.082(atm*L)/(mol*K)*298K)/(0.941atm)\\\\M=44.06(g)/(mol)`

Thus, the gas may be propane (
`C_3H_8`) since it molar mass is 44.11 g/mol.

Best regards!