Natural gas is mixture of hydrocarbons, primarily methane(CH4) and ethane(C2H6).

Question

Natural gas is mixture of hydrocarbons, primarily methane(CH4) and ethane(C2H6). A typical mixture might have Xmethane=0.915 and Xethane=0.085. Let's assume that we have a 15.25g sample of natural gas in a volume of 14.85L at a temperature of 21.25C degrees. A.how total many moles of gas are in the sample? B.what is the pressure of the sample( in atmospheres)? C.what is the partial pressure of each component in the sample(in atmospheres)? D.when sample is burned in a excess of oxygen, how much heat (in kilojoules) is liberated? Natural gas is mixture of hydrocarbons, primarily methane(CH4) and ethane(C2H6). A typical mixture might have Xmethane=0.915 and Xethane=0.085. Let's assume that we have a 15.25g sample of natural gas in a volume of 14.85L at a temperature of 21.25C degrees. A.how total many moles of gas are in the sample? B.what is the pressure of the sample( in atmospheres)? C.what is the partial pressure of each component in the sample(in atmospheres)? D.when sample is burned in a excess of oxygen, how much heat (in kilojoules) is liberated? A.how total many moles of gas are in the sample? B.what is the pressure of the sample( in atmospheres)? C.what is the partial pressure of each component in the sample(in atmospheres)? D.when sample is burned in a excess of oxygen, how much heat (in kilojoules) is liberated?

Explanation / Answer

A.  Let x = the total moles of gas.

Then 0.915x = moles of methane and 0.085x = moles of ethane.

Grams of methane + grams of ethane = 15.25 g
(0.915x moles CH4)(16.0 g/mol CH4 ) + (0.085x moles C2H6)(30.0 g/mol C2H6 ) = 15.50

14.6x + 2.55x = 15.50
17.2x = 15.5
x = 0.904 moles

Tatol moles of gas = 0.904 moles

moles of methane = 0.82716 moles

moles of ethane = 0.07684 moles

B. PV = nRT

P = nRT / V { R = 0.082 L atm / K.mol T = 273.15 +21.25 = 294.4 K}

P = (0.904 x 0.082 x 294.4 / 14.85 L) = 1.4695 atm

C. partial pressure = mole fraction x total pressure

partial pressure of methane = (1.4695 atm x 0.915 ) = 1.3446 atm

partial pressure of ethane = (1.4695 atm x 0.085) = 0.1249 atm

D. methane deltaH= -802 kJ/mol
ethane deltaH= -1561 kJ/mol

total  heat (in kilojoules) is liberated = (-802 x 0.82716 moles) + (-1561 x 0.07684 moles) = -783.33 KJ

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