Question

Consider the combustion of propane: A balloon is being inflated to its full extent by heating the air inside it. In the final stages of this process, the volume of the balloon changes from L to L by the addition of J energy as heat. Assume that all the heat comes from the combustion of propane. What mass of propane must be burned to furnish this amount of energy assuming the heat transfer process is 50.% efficient?

Answer 1

Hi you have missed key values for this, no problem, i found them here in below links, if they are not matched with your values please inform to me below at comments section.

http://www.lundquistlabs.com/uploads/3/0/3/6/3036736/unit_d_packet_2016.pdf        (Exercise 3)

http://tns.ndhu.edu.tw/~ichem/subject/update_subject/chen/CH06.pdf           (Page 28, sample exercise 6.3)

http://www.myteacherpages.com/webpages/apchem/files/Heat,%20Energy%20and%20Work.pdf    (Exercise 3)

Δ E = q + w. and given q = +1.3 x 10⁸ J.

w = -P. ΔV ( Given P = 1 atm and ΔV = V_initial – V_final) = 4.5 x 10⁶ L - 4.00 x 10⁶ L = 5.0 x 10⁵ L.

w = -1.0 atm * 5.0 x 10⁵ L = - 5.0 x 10⁵ L atm. (the negative sign is because the gas is expanding and doing work on the surroundings).

Convert w to J (1 L. atm = 101.3 J);

w = -5.0 x 10⁵ L atm * (101.3 J / L atm) = -5.065 x 10⁷ J.

Δ E = q + w = (+1.3 x 10⁸ J) + (-5.065 x 10⁷ J) = 7.935 x 10⁷ J.

Since more energy is added through heating than the gas expends doing work, there is a net increase in the internal energy of the gas in the balloon. Hence ΔE is positive.

C₃H₈(g) + 5O₂(g) ----> 3CO₂ (g) + 4H₂O (l) ΔH = -2221 kJ

If 50% efficient we need double energy = 2 x 7.935 x 10⁷ J = 15.87 x 10⁷ J

1 mole propane gives 2221 kJ energy = 2221000 J

moles propane required = 15.87 x 10⁷ J / 2221000 J = 71.4542998649 mol

convert moles to mass of propane = moles propane required x molar mass of propane

mass of propane must be burned = 71.4542998649 mol x 44.1 g/mol = 3151.13462404 g = 3.15 x 10³ g

mass of propane must be burned to furnish this amount of energy assuming the heat transfer process is 50.% efficient = 3.15 x 10³ g

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