This question is about the unnecessary production of carbon dioxide

Outdoor flames, such as patio heaters and the Olympic flame, contribute to global warming. This is not only due to the heat released, but also due to the carbon dioxide produced from the
combustion of hydrocarbons. Most patio heaters are powered by small cylinders of propane gas. A typical patio heater designed to produce 15 kW of energy runs from a cylinder containing 13 kg of propane. A ‘completely full’ cylinder at a pressure of 140 psi (9.52 atmospheres) is in fact only filled to about 87% capacity with liquid propane, the remaining volume being taken up by propane vapour. The standard enthalpy change of combustion of propane is –2220 kJ mol–1.

Assume 1 mole of a gas occupies 24 dm3 under the conditions of this question.

i) Calculate the number of moles of propane contained in a cylinder.
ii) Calculate the mass of carbon dioxide produced when all of the propane in a cylinder
is burnt completely.
iii) Calculate the total amount of heat energy released by combustion of all the propane
in a cylinder.

i. Convert 13,000 grams Propane (C3H8) to moles

ii. write the balanced equation
2C3H8+ 10O2 >>> 6CO2 + 8H2O
so the moles you had in i, you should have twice that number of moles of carbon dioxide. Convert that to mass.

iii. for each moles in i, multiply by 2220kj

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To answer these questions, we need to follow a step-by-step approach and use the given information.

i) Calculate the number of moles of propane contained in a cylinder:

We are given that the cylinder contains 13 kg of propane. To convert this mass into moles, we need to use the molar mass of propane. The molar mass of propane (C3H8) is calculated as follows:
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
Total molar mass of propane (C3H8) = 3 * (12.01 g/mol) + 8 * (1.01 g/mol) = 44.11 g/mol.

Now we can calculate the number of moles using the following formula:
Number of moles = Mass / Molar mass.

Substituting the values, we get:
Number of moles = 13,000 g / 44.11 g/mol = 294.63 mol.

Therefore, the number of moles of propane contained in a cylinder is approximately 294.63 mol.

ii) Calculate the mass of carbon dioxide produced when all of the propane in a cylinder is burnt completely:

The balanced chemical equation for the combustion of propane is:
C3H8 + 5O2 -> 3CO2 + 4H2O.

From the equation, we can see that 1 mole of propane produces 3 moles of carbon dioxide.
Therefore, the mass of carbon dioxide produced is calculated as follows:
Mass of CO2 = Number of moles of propane * 3 * Molar mass of CO2.

The molar mass of carbon dioxide (CO2) is calculated as follows:
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of oxygen (O) = 16.00 g/mol
Total molar mass of carbon dioxide (CO2) = 12.01 g/mol + 2 * (16.00 g/mol) = 44.01 g/mol.

Substituting the values, we get:
Mass of CO2 = 294.63 mol * 3 * 44.01 g/mol = 38,883.18 g.

Therefore, the mass of carbon dioxide produced when all of the propane in a cylinder is burnt completely is approximately 38,883.18 g or 38.88 kg.

iii) Calculate the total amount of heat energy released by combustion of all the propane in a cylinder:

The standard enthalpy change of combustion of propane is given as -2220 kJ/mol.

The total amount of heat energy released by the combustion of all the propane is calculated as follows:
Heat energy = Number of moles of propane * Enthalpy change of combustion of propane.

Substituting the values, we get:
Heat energy = 294.63 mol * -2220 kJ/mol = -653,728.6 kJ.

Therefore, the total amount of heat energy released by the combustion of all the propane in a cylinder is approximately -653,728.6 kJ or 653,728.6 kJ (since the enthalpy change is negative).