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what mass of CO_2 is emitted into the atmosphere during the grilling of the pork roast

The propane fuel C_3H_8 used in gas barbeques burns according to the following thermochemical equation:
C_3 H_8 (g) + 5O_2 (g) right arrow 3CO_2 (g) + 4H_2 O(g) Delta H= -2217kJ

If a pork roast must absorb 1700 kJ to fully cook, and if only 14% of the heat produced by the barbeque is actually absorbed by the roast, what mass of CO_2 is emitted into the atmosphere during the grilling of the pork roast?

The amount of heat needed to cook the pork roast is 1700 kJ.

The amount of heat absorbed by the roast is 14% of the heat produced  = 14% X ?H = 310.38 kJ/mol

One mole of propane burns to produce 3 moles of CO2 and -2217 kJ of heat.

1700kJ/ (14% X ?H) = mol of C3H8 burned

1700kJ / (310.38 kJ/mol) = 5.48 mol C3H8

Since 3 moles of CO2 are produced:

3 X 5.48 mol= 16.43 mols of CO2

convert moles to grams:

16.43 mol CO2 X 44.0g/mol ~ 722.9 g CO2 produced