LP gas burns according to the exothermic reaction: C3H8( g) + 5 O2( g)¡3 CO2( g) + 4 H2O( g) ΔH °rxn = -2044 kJ What mass of LP gas is necessary to heat 2.50 L of water from room temperature (25.0 °C) to boiling (100.0 °C)? Assume that during heating, 15% of the heat emitted by the LP gas combustion goes to heat the water. The rest is lost as heat to the surroundings. (Assume a density of 1.00 g/mL for water.)

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Calculate the amount of heat required to raise the temperature of the water. Use the formula: \(Q = mc\Delta T\), where \(m\) is the mass of the water, \(c\) is the specific heat capacity of water (approximately 4.18 J/g°C), and \(\Delta T\) is the change in temperature.

Convert the volume of water to mass. Since the density of water is given as 1.00 g/mL, the mass of 2.50 L of water can be calculated as 2500 g (since 1 L = 1000 mL).

Calculate the total heat required by the water using the mass from step 2, the specific heat capacity of water, and the temperature change from 25.0 °C to 100.0 °C.

Determine the total heat that needs to be produced by the LP gas combustion, considering that only 15% of the heat is used to heat the water. Divide the heat calculated in step 3 by 0.15 to account for the heat loss.

Calculate the mass of LP gas required using the heat of reaction (ΔH°rxn). The heat of reaction for the combustion of LP gas is given as -2044 kJ per mole of C3H8. Use the formula: \(m = \frac{Q}{\Delta H_{rxn} \times \text{molar mass of C3H8}}\) to find the mass of LP gas needed, where \(Q\) is the total heat required from step 4.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exothermic Reactions

Exothermic reactions are chemical processes that release energy, usually in the form of heat, to the surroundings. In the given reaction, the combustion of propane (C3H8) releases -2044 kJ of energy. Understanding this concept is crucial for calculating how much energy is available to heat water and how much of that energy is effectively used.

Heat Transfer and Specific Heat Capacity

Heat transfer refers to the movement of thermal energy from one object to another, which is essential in heating processes. The specific heat capacity of water, which is 4.18 J/g°C, indicates how much energy is required to raise the temperature of 1 gram of water by 1°C. This concept is vital for determining how much energy is needed to heat the specified volume of water from 25.0 °C to 100.0 °C.

Mass and Energy Calculations

Mass and energy calculations involve using stoichiometry and the principles of conservation of energy to relate the mass of a substance to the energy it can produce or absorb. In this scenario, calculating the mass of LP gas needed requires converting the energy available from combustion into the mass of propane, considering that only 15% of the heat is used to heat the water. This concept is essential for solving the problem accurately.

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