Ch.6 - Thermochemistry

Problem 100

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Chapter 6, Problem 100

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 1.5 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.

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Calculate the amount of heat required to raise the temperature of 1.5 L of water from 25.0 °C to 100.0 °C using the formula: \( q = m \cdot c \cdot \Delta T \), where \( m \) is the mass of water, \( c \) is the specific heat capacity of water (4.18 J/g°C), and \( \Delta T \) is the change in temperature.

Convert the volume of water (1.5 L) to mass in grams, knowing that the density of water is approximately 1 g/mL.

Calculate the total heat required in kilojoules by converting the result from step 1 from joules to kilojoules.

Determine the total heat emitted by the combustion of LP gas needed to provide the calculated heat to the water, considering that only 15% of the heat is used to heat the water. Use the formula: \( \text{Total heat emitted} = \frac{\text{Heat required}}{0.15} \).

Calculate the mass of LP gas needed using the enthalpy change of the reaction (\( \Delta H^\circ_{\text{rxn}} = -2044 \text{ kJ/mol} \)) and the molar mass of propane (C3H8). Use the formula: \( \text{Mass of LP gas} = \frac{\text{Total heat emitted}}{\Delta H^\circ_{\text{rxn}}} \times \text{Molar mass of C3H8} \).

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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 per mole, indicating that this energy can be harnessed for heating purposes. Understanding this concept is crucial for calculating how much energy is available for heating water.

Heat Transfer and Specific Heat Capacity

Heat transfer refers to the movement of thermal energy from one object or substance to another. The specific heat capacity of a substance, such as water, quantifies how much heat is required to raise its temperature by a certain amount. For water, the specific heat capacity is approximately 4.18 J/g°C, which is essential for determining how much energy is needed to heat 1.5 L of water from 25.0 °C to 100.0 °C.

Energy Efficiency in Heating

Energy efficiency in heating refers to the proportion of energy that is effectively used for the intended purpose, in this case, heating water. The problem states that only 15% of the heat produced by the combustion of LP gas is used to heat the water, meaning that the calculations must account for this efficiency to determine the actual amount of propane needed to achieve the desired temperature increase.

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Related Practice

The kinetic energy of a rolling billiard ball is given by KE = 1/2 mv². Suppose a 0.17-kg billiard ball is rolling down a pool table with an initial speed of 4.5 m/s. As it travels, it loses some of its energy as heat. The ball slows down to 3.8 m/s and then collides head-on with a second billiard ball of equal mass. The first billiard ball completely stops and the second one rolls away with a velocity of 3.8 m/s. Assume the first billiard ball is the system. Calculate q.

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Open Question

A 100-W lightbulb is placed in a cylinder equipped with a moveable piston. The lightbulb is turned on for 0.015 hour, and the assembly expands from an initial volume of 0.85 L to a final volume of 5.88 L against an external pressure of 1.0 atm. Use the wattage of the lightbulb and the time it is on to calculate ΔE in joules (assume that the cylinder and lightbulb assembly is the system and assume two significant figures). Calculate w. Calculate q.

Open Question

Evaporating sweat cools the body because evaporation is an endothermic process: H2O(l) → H2O(g) ΔH°rxn = +44.01 kJ. Estimate the mass of water that must evaporate from the skin to cool the body by 0.50°C. Assume a body mass of 95 kg and assume that the specific heat capacity of the body is 4.0 J/g°C.

Textbook Question

Use standard enthalpies of formation to calculate the standard change in enthalpy for the melting of ice. (The ΔH°_f for H₂O(s) is –291.8 kJ/mol.)

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Textbook Question

Use standard enthalpies of formation to calculate the standard change in enthalpy for the melting of ice. (The ΔH°_f for H₂O(s) is –291.8 kJ/mol.) Use this value to calculate the mass of ice required to cool 355 mL of a beverage from room temperature (25.0 °C) to 0.0 °C. Assume that the specific heat capacity and density of the beverage are the same as those of water.

Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the equation: CO₂(s) → CO₂(g) ◀ When carbon dioxide sublimes, the gaseous CO₂ is cold enough to cause water vapor in the air to condense, forming fog. When dry ice is added to warm water, heat from the water causes the dry ice to sublime more quickly. The evaporating carbon dioxide produces a dense fog often used to create special effects. In a simple dry ice fog machine, dry ice is added to warm water in a Styrofoam cooler. The dry ice produces fog until it evaporates away, or until the water gets too cold to sublime the dry ice quickly enough. Suppose that a small Styrofoam cooler holds 15.0 L of water heated to 85 °C. Use standard enthalpies of formation to calculate the change in enthalpy for dry ice sublimation, and calculate the mass of dry ice that should be added to the water so that the dry ice completely sublimes away when the water reaches 25 °C. Assume no heat loss to the surroundings. (The ΔH°_f for CO₂(s) is –427.4 kJ/mol.)

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