Ch.5 - Thermochemistry

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.5 - Thermochemistry

Problem 51d

Chapter 5, Problem 51d

(d) How many kJ of heat are needed to raise the temperature of 10.00 kg of liquid water from 24.6 to 46.2 °C?

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Identify the formula to calculate the heat required to change the temperature of a substance: \( q = mc\Delta T \), where \( q \) is the heat energy, \( m \) is the mass, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.

Determine the specific heat capacity of liquid water, which is typically \( 4.18 \text{ J/g°C} \).

Convert the mass of water from kilograms to grams, since the specific heat capacity is given in \( \text{J/g°C} \). For 10.00 kg, this is \( 10,000 \text{ g} \).

Calculate the change in temperature \( \Delta T \) by subtracting the initial temperature from the final temperature: \( 46.2°C - 24.6°C \).

Substitute the values into the formula: \( q = (10,000 \text{ g})(4.18 \text{ J/g°C})(\Delta T) \) and convert the result from joules to kilojoules by dividing by 1,000.

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Key Concepts

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

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. For water, this value is approximately 4.18 J/g°C. Understanding this concept is crucial for calculating the heat energy needed for temperature changes in substances.

Heat Transfer Equation

The heat transfer equation, often expressed as q = mcΔT, relates the heat energy (q) absorbed or released by a substance to its mass (m), specific heat capacity (c), and the change in temperature (ΔT). This equation is fundamental for solving problems involving temperature changes in materials.

Units of Energy

Energy is commonly measured in joules (J) or kilojoules (kJ), where 1 kJ equals 1000 J. In thermodynamics, it is important to be consistent with units when performing calculations, especially when converting between different energy units to ensure accurate results.

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Related Practice

Textbook Question

b. What are the units of specific heat?

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Textbook Question

Consider the decomposition of liquid benzene, C₆H₆(l), to gaseous acetylene, C₂H₂(g): C₆H₆(l) → 3 C2H₂(g) ΔH = +630 kJ (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction?

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Textbook Question

Consider the data about gold metal in Exercise 5.24(b). b. Suppose that the same amount of heat is added to two 10.0-g blocks of metal, both initially at the same temperature. One block is gold metal, and the other is iron metal. Which block will have the greater rise in temperature after addition of the heat?

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Textbook Question

The specific heat of ethanol, C₂H₅OH(l), is 2.44 J•g/K. b. Which will require more heat, increasing the temperature of 1 mol of C₂H₅OH(𝑙) by a certain amount or increasing the temperature of 1 mol of H₂O(𝑙) by the same amount?

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Textbook Question

Two solid objects, A and B, are placed in boiling water and allowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing 1000 g of water at 10.0 °C. Object A increases the water temperature by 3.50 °C; B increases the water temperature by 2.60 °C. (a) Which object has the larger heat capacity?

(b) Calculate the energy needed for this temperature change.

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