Question

A sample of a gas with a volume of 745 cm3 at a temperature of 35.0°C and pressure of 100 kPa has a mass of 2.51 g. The gas is 83.6% carbon and 16.4% hydrogen by mass. Find the molecular formula

Answer 1

A sample of a gas with a volume of 745 cm³ at a temperature of 35.0°C and pressure of 100 kPa has a mass of 2.51 g. the gas has 83.6 % carbon and 16.4% hydrogen by mass.

We have to find the molecular formula of the gas.

first we should find the number of moles of gas using equation of gas.

here, volume of gas, V = 745 cm³ = 0.745 L [ ∵ 1000 cm³ = 1 L ]

the temperature of gas, T = 35°C = 35 + 293 = 328 K

pressure of gas, P = 100 kPa = 0.987 atm [ ∵ 1 atm = 1.013 × 10⁵ Pa ]

using gas equation, PV = nRT

⇒ 0.987 atm × 0.745 L = n × 0.082 L.atm/mol/L × 328K

⇒ n = 0.027339 mol

given the mass gas = 2.51 g

∴ molecular mass of gas = mass of gas/no of moles of gas

= 2.51/0.027339  ≈ 92 g/mol

here, 83.6% carbon and 16.4% hydrogen present in the gas.

ratio of percent/atomic mass of each term.

for carbon ⇒ 83.6/12 = 6.966

for hydrogen ⇒ 16.4/1 = 16.4

the simplest ratio of carbon and hydrogen is ..

C : H = 6.966 : 16.4 = 3 : 7

so empirical formula is C₃H₇

∵  molar mass = n × empirical mass

⇒ 92 = n × ( 3 × 12 + 7 × 1 )

⇒ 92 = n × 46

⇒ n = 92/46 = 2

∴ molecular formula of gas = 2(C₃H₇) = C₆H₁₄

Therefore the molecular formula of the gas is C₆H₁₄.