QUESTION 1: THERMOCHEMISTRY
a) An LP gas tank in a home barbeque contains 13.2 kg of propane, [tex]C _3 H _8[/tex]. Calculate the heat (in kJ ) associated with the complete combustion of all of the propane in the tank.
[tex]C_3 H_8(g)+5 O_2(g) \longrightarrow 3 CO_2(g)+4 H_2 O(g) \Delta H_{run}=-2044 kJ[/tex]
Answer (2)
Calculate the molar mass of propane ( C 3 H 8 ) using the molar masses of carbon and hydrogen.
Convert the mass of propane from kg to grams.
Calculate the number of moles of propane using the formula: m o l es = m o l a r ma ss ma ss .
Calculate the total heat released by multiplying the number of moles of propane by the enthalpy of reaction: T o t a l He a t = m o l es × Δ H r x n .
The heat associated with the complete combustion of all of the propane in the tank is − 611892.77 k J .
Explanation
Understanding the Problem We are given the mass of propane ( C 3 H 8 ) in an LP gas tank and the enthalpy change ( Δ H r x n ) for the complete combustion of propane. We need to calculate the total heat associated with the combustion of all the propane in the tank.
Calculating Molar Mass of Propane First, we need to calculate the molar mass of propane ( C 3 H 8 ). The molar mass of carbon (C) is approximately 12.01 g/mol, and the molar mass of hydrogen (H) is approximately 1.008 g/mol. Therefore, the molar mass of propane is: M o l a r M a ss ( C 3 H 8 ) = ( 3 × 12.01 ) + ( 8 × 1.008 ) = 36.03 + 8.064 = 44.094 g / m o l
Converting Mass to Grams Next, we convert the mass of propane from kilograms to grams: M a ss ( p ro p an e ) = 13.2 k g = 13.2 × 1000 g = 13200 g
Calculating Moles of Propane Now, we calculate the number of moles of propane using the formula: M o l es = M o l a r M a ss M a ss = 44.094 g / m o l 13200 g = 299.36 m o l
Using Enthalpy of Reaction We are given the enthalpy change for the combustion of propane: Δ H r x n = − 2044 k J / m o l . This means that when one mole of propane is combusted, 2044 kJ of heat is released.
Calculating Total Heat Released To find the total heat released, we multiply the number of moles of propane by the enthalpy change: T o t a l He a t = M o l es × Δ H r x n = 299.36 m o l × ( − 2044 k J / m o l ) = − 611892.77 k J
Final Answer The negative sign indicates that the reaction is exothermic, meaning heat is released. Therefore, the heat associated with the complete combustion of all the propane in the tank is approximately 611892.77 kJ.
Final Answer Therefore, the heat associated with the complete combustion of all of the propane in the tank is approximately − 611892.77 k J .
Examples
Thermochemistry is crucial in various real-world applications, such as designing efficient engines and understanding energy production. For instance, when designing a propane-fueled barbeque, engineers need to calculate the amount of heat produced during combustion to ensure the grill reaches the desired temperature. By knowing the mass of propane in the tank and the enthalpy of combustion, they can accurately predict the total heat output. This calculation helps in optimizing the design for safety and performance, ensuring the barbeque operates efficiently and effectively. Understanding these principles allows for better control and utilization of energy in everyday appliances and industrial processes.
The heat associated with the complete combustion of 13.2 kg of propane is approximately -611892.77 kJ, indicating that the reaction is exothermic. This involves calculating the molar mass, converting mass to moles, and applying the enthalpy change for combustion. The total heat released reflects the energy contributed by combusting all the propane in the tank.
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