# 利用氣體密度計算得知氣體分子式

What us the molar mass of a gaseous alkane hydrocarbon having a density of 2.42 g/L at 20℃ and 762 Torr?

What is the molecular formula of the gas?

Rating

According to the theory of ideal gas, the volume of one mole gas under standard conditions (0 degree C and 1 atm) should be 22.4L. If the temperature is raised to 20 degree C, the volume of the gas (Vt) will be expanded.

Vt = Vo*[1 (t/273)]

Vt = 22.4 L*[1 (20/273)]

Vt = 24.04 L (<-- the gas volume at 20 degree C and 760 torr)

However, if the pressure of the gas is raised, the volume of the gas will be reduced. (Note: 1 atm = 760 torr)

P1V1 = P2V2

1 atm*24.04 = (762/760)*V2

V2 = 23.98 L (<--the gas volume at 762 torr and 20 degree C)

Therefore, the molar mass of the gas you indicated will be:

Molar mass = 2.42 g/L * 23.98 L = 58.02 g (for the FIRST ANSWER)

The molecular formula of the gass should be CnH2n 2

Therefore, 12*n 1*(2n 2) = 58.02

14*n 2 = 58.02

n = 4

The molecular formula of the gas should be C4H10 (for the SECOND ANSWER)

2008-10-29 20:28:37 補充：

A minor correction for the part of the second answer:

The molecular formula of the gass should be CnH2n + 2

Therefore, 12*n + 1*(2n + 2) = 58.02

14*n 2 = 58.02

n = 4

The molecular formula of the gas should be C4H10 (for the SECOND ANSWER)