Part A A gaseous fuel mixture contains 253 methane CH4 382 e

Part A A gaseous fuel mixture contains 25.3% methane (CH4), 38.2% ethane (C2H6). and the rest propane (CsHs) by volume. When the fuel mixture contained in a 1.49 L tank, stored at 779 mmHg and 298 K, undergoes complete combustion, how much heat is emitted? (Assume that the water produced by the combustion is in the gaseous state.) Express your answer with the appropriate units Valuekj

Solution

Ans. Step 1: Determine total moles of gas in the tank

Given

            Volume, V = 1.49 L

            Temperature, T = 298 K

            Pressure, P = 779 mm Hg = (779 / 760) atm = 1.025 atm

Using Ideal gas equation:    PV = nRT      - equation 1

            Where, P = pressure in atm

            V = volume in L                   

            n = number of moles

            R = universal gas constant= 0.0821 atm L mol^-1K^-1

            T = absolute temperature (in K) = (⁰C + 273.15) K

Putting the values in above equation-

            1.025 atm x 1.49 L = n x (0.0821 atm L mol^-1K^-1) x 298 K

            Or, n = 1.52725 atm L / (24.4658 atm L mol^-1)

            Hence, n = 0.0624 mol

# Step 2: Determine moles of each gas in the tank:

Following Avogadro’s Law, equal volume of all gases have equal number of moles, at constant pressure and temperature. So, volume % of gases is equal to their respective mole %.

Now,

            Moles of methane = 25.3 % of 0.0624 mol = 0.0157872 mol

            Moles of ethane = 38.2 % of 0.0624 mol = 0.0238368 mol

            Moles of propane = (100 – 25.3 – 38.2) % of 0.0624 mol = 0.022776 mol

# Step 3: Determine amount of heat released:

# Heat released from methane = Moles of methane x Molar enthalpy of combustion

                                                = 0.0157872 mol x (-890 kJ mol^-1)

                                                = 14.050608 kJ

# Heat released from ethane = 0.0238368 mol x (-1560 kJ mol^-1) = 37.185408 kJ

# Heat released from propane = 0.022776 mol x (-2220 kJ mol^-1) = 50.56272 kJ

Total heat released = 14.050608 kJ + 37.185408 kJ + 50.56272 kJ = 101.8 kJ