Answer to Question #68923 in Molecular Physics | Thermodynamics for DEEPENDRA SINGH

Question

a pure gass which contains 14.3% hydrogen and 85.7% carbon of total mass.its density is 2.5 gram per leter at 0 degree centigrate and 1 atm.what is it molecular formula?

Answer 1

From the equation of state for perfect gas
PV=m/M RT
We obtain the expression for the density of gas
ρ=m/V=PM/RT.
Therefore the molar mass of gas is
M=ρRT/P=(2.5×8.3×273)/(1.01×〖10〗^5 )=56 g/mol.
Because
M(H)=1 g/mol,M(C)=12 g/mol.
We obtain
14.3/85.7×12=2.
So the number of hydrogen atoms is twice of carbon.
Because the molar mass of gas is 56, we obtain equation for the number of carbon atoms x
2×1×x+12×x=56 ⇒ x=4.
So the molecular formula of the gas is
C_4 H_8
Answers: C_4 H_8