Question

The analysis of a hydrocarbon revealed that it was 85.7% C and 14.3% H by mass. When 1.77 g of the gas was stored in a 1.500-L fl ask at 17 ?C, it exerted a pressure of 508 Torr. What is the molecular formula of the hydrocarbon?

Answer 1

The formula of hydrocarbon =
`C_3H_6`

Step-by-step explanation:

`Moles =\frac {Given\ mass}{Molar\ mass}`

% of C = 85.7

Molar mass of C = 12.0107 g/mol

% moles of C = 85.7 / 12.0107 = 7.14

% of H = 14.3

Molar mass of H = 1.00784 g/mol

% moles of H = 14.3 / 1.00784 = 14.19

Taking the simplest ratio for C and H as:

7.14 : 14.19 = 1 : 2

The empirical formula is =
`CH_2`

Also, Given that:

Pressure = 508 Torr

Temperature = 17 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15

So,

T = (17 + 273.15) K = 290.15 K

Volume = 1.500 L

Using ideal gas equation as:

`PV=nRT`

where,

P is the pressure

V is the volume

n is the number of moles

T is the temperature

R is Gas constant having value = 62.3637 L.torr/K.mol

Applying the equation as:

508 Torr × 1.500 L = n × 62.3637 L.torr/K.mol × 290.15 K

⇒n = 0.0421 moles

Given that :

Amount = 1.77 g

Molar mass = ?

The formula for the calculation of moles is shown below:

`moles = (Mass\ taken)/(Molar\ mass)`

Thus,

`0.0421\ moles= (1.77\ g)/(Molar\ mass)`

Molar mass of the hydrocarbon = 42.04 g/mol

Molecular formulas is the actual number of atoms of each element in the compound while empirical formulas is the simplest or reduced ratio of the elements in the compound.

Thus,

Molecular mass = n × Empirical mass

Where, n is any positive number from 1, 2, 3...

Mass from the Empirical formula = 1×12 + 2×1= 14 g/mol

Molar mass = 42.04 g/mol

So,

Molecular mass = n × Empirical mass

42.04 = n × 14

⇒ n = 3

The formula of hydrocarbon =
`C_3H_6`