The formula of the hydrocarbon gas is C₃H₈.
Using the ideal gas equation:
PV = nRT
From the given values:
Pressure of gas = 540.5 mmHg
Converting pressure in mmHg to atm:
1 atm = 760 mmHg
540.5 mmHg = 540.5 mmHg * 1 atm/760 mmHg
pressure = 0.711 atm
Pressure, P of gas in atm = 0.711 atm
Volume, V of gas = 8.18 L
T, temperature of gas in Kelvin = 40.2 + 273.15 K = 313.35 K
number of moles, n = mass /molar mass
mass of gas = 9.98; molar mass = x
Substituting mass /molar mass for n in the Ideal gas equation:
PV = RT* mass/molar mass
making molar mass subject of the formula
molar mass = mass* RT/ PV
molar mass of gas = (9.98 * 0.082 * 313.35) / 0.711 * 8.18
molar mass of gas = 44.09 g/mol
Since the gas is a hydrocarbon, it is composed of carbon and hydrogen alone.
The hydrocarbon gas that has a molar mass of 44.0 g is C₃H₈.
Therefore, the formula of the hydrocarbon gas is C₃H₈.
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