To find the molecular formula of the gas, its molecular weight must be calculated.
According to the ideal gas law:
pV = nRT or pV = mRT / Mr
where p - pressure, V - volume, n - number of moles, R - gas constant, T - temperature, m - mass, Mr - molecular weight.
Mr = mRT / pV
As R = 0.082057 L atm / K mol and T = 110.0 °C = 383.15 K:
Mr(gas) = (0.72 g × 0.082057 L atm / K mol × 383.15 K) / (0.967 atm × 0.417 L) = 56 g/mol
As a result, molecular weight of the gas is 56 g/mol and its empirical formula is CH2. From here:
(12g/mol × x) + (2 × 1 g/mol × x) = 56 g/mol
where x - index coeeficient, 12g/mol and 1 g/mol - molecular weight of carbon and hydrogn respectively. From here:
12x + 2x = 56
14x = 56
x = 4
As a result, the molecular formula of the gas is C4H8