Question

The composition of a particular natural gas, expressed on a mole fraction basis, is CH4, 0.830; C2H6, 0.112; C3H8, 0.058. A 2.15 L sample of this natural gas, measured at 24.5 degrees Celsius and 744 mmHg is burned in an excess of oxygen. How much heat is evolved in the combustion?

Answer 1

There is 89.9 kJ of heat evolved in the combustion

Step-by-step explanation:

Step 1: Data given

Mole fraction of CH4 = 0.830

Mole fraction of C2H6 = 0.112

Mole fraction of C3H8 = 0.058

Volume = 2.15 L

Temperature = 24.5 °C = 297.65 Kelvin

744 mmHg is burned

The combustion of methane (CH4) releases 891 kJ of energy

The combustion of ethane (C2H6) releases 1561 kJ of energy

The combustion of propane (C3H8) releases 2220 kJ of energy

Step 2: Calculate number of moles of

p*V= n*R*T

⇒ p = The pressure = 744 mmHg = 744/760 = 0.979 atm

⇒ V = the volume = 2.15 L

⇒ n= The number of moles = TO BE DETERMINED

⇒ R = the gas constant = 0.08206 L*atm/k*mol

⇒ T = The temperature = 24.5 °C = 297.65 Kelvin

n(total) = PV / RT = (0.979 *2.15 ) / (0.08206 * 297.65 )

n(total) = 0.0862 moles

Step 3: Calculate energy for combustion of each gas

CH4: 0.0862 moles * 0.830 * 891 kJ/mol = 63.7 kJ

C2H6: 0.0862 moles * 0.112 * 1561 kJ/mol = 15.07 kJ

C3H8: 0.0862 moles * 0.0580 * 2220 kJ/mol = 11.1 kJ

Step 4: Calculate tot heat for the combustion

63.7 kJ + 15.07 kJ + 11.1 kJ = 89.9 kJ total

There is 89.9 kJ of heat evolved in the combustion