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Chapter 6: Problem 101

When a \(6.00-\mathrm{g}\) sample of coal is burned, it releases enough heat to raise the temperature of \(2010 \mathrm{~g}\) of water from \(24.0^{\circ} \mathrm{C}\) to \(41.5^{\circ} \mathrm{C}\). (a) How much heat did the coal release as it burned? (b) Calculate the heat of combustion of coal in units of \(\mathrm{kJ} / \mathrm{g}\).

Short Answer

Expert verified
(a) The heat released by the coal is approximately \(146.065 \mathrm{kJ}\). (b) The heat of combustion for the coal is approximately \(24.344 \mathrm{kJ/g}\).

Step by step solution

01

Calculate the Heat Released (A)

To calculate the heat released by the coal, you have to use the formula \(q = mc\Delta T\), where \(q\) is the heat, \(m\) is the mass, \(c\) is the specific heat, and \(\Delta T\) is the change in temperature. For water, \(c\) is typically \(4.18 \mathrm{J/g\cdot C}\). The mass of the water is given as \(2010 \mathrm{g}\) and the temperature increase (\(\Delta T\)) is \(41.5^{\circ} \mathrm{C} - 24.0^{\circ} \mathrm{C} = 17.5^{\circ} \mathrm{C}\). So, the heat released (\(q\)) is \(2010 \mathrm{g} \cdot 4.18 \mathrm{J/g\cdot C} \cdot 17.5^{\circ} \mathrm{C}\).
02

Convert Joules to Kilojoules

The result from the previous calculation will be in joules (J). However, we need the result in kilojoules for the next step. To convert joules to kilojoules, simply divide the result by 1000.
03

Calculate the Heat of Combustion (B)

To calculate the heat of combustion per gram, you use the formula \(q/m_{coal}\), where \(q\) is the heat released by the coal (in kJ) and \(m_{coal}\) is the mass of the burned coal. Alert: the mass of coal should in grams which is given as \(6 \mathrm{g}\). Therefore, the heat of combustion would be calculated by taking the heat released (obtained from previous parts and converted to kJ) and dividing it by the mass of the coal.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermochemistry
Thermochemistry is the study of the heat energy involved in chemical reactions and physical changes. It's a fundamental concept that helps us understand how energy is absorbed or released when substances react or change their physical state. The central theme in thermochemistry is the law of conservation of energy, stating that energy can neither be created nor destroyed. In the context of our coal combustion example, the energy released when coal burns is absorbed by the surrounding water, causing the water temperature to rise.
Specific Heat Capacity
Specific heat capacity, often simply referred to as specific heat, is an intrinsic property of a substance that indicates how much heat energy is required to raise the temperature of one gram of the substance by one degree Celsius. It is denoted by the symbol 'c' and is measured in units of joules per gram per degree Celsius (J/g掳C). In our coal burning scenario, water has a specific heat capacity of 4.18 J/g掳C, which means that 4.18 joules are needed to raise the temperature of 1 gram of water by 1掳C. This property is crucial for calculating the amount of heat absorbed by the water as it is heated by the energy released from coal combustion.
Energy Conversion
Energy conversion is the process of changing one form of energy into another. In chemical reactions, such as the combustion of coal, chemical energy stored in the bonds of the reactants is converted into heat energy. This conversion is central to many industrial and everyday processes, including the generation of electricity and the heating of homes. In the exercise, the chemical energy in coal is converted into thermal energy that is transferred to water, increasing its temperature. It's key to recognize that during these conversions, the total amount of energy is conserved, aligning with the principle of energy conservation.
Chemical Thermodynamics
Chemical thermodynamics deals with the relationship between heat, work, and chemical reactions. It is the science that quantifies the energy transformations in systems as they undergo physical changes or chemical reactions. The heat of combustion, as seen in our example, is a thermodynamic property and it represents the heat released when a substance undergoes complete combustion in the presence of oxygen at a constant pressure. The calculated heat of combustion for coal provides valuable information about its energy content, which is essential for assessing its efficiency as a fuel.

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Most popular questions from this chapter

When a chemical reaction occurs in a calorimeter containing water, and the temperature of the water decreases, is the reaction endothermic or exothemic?

A student added zine metal to a copper nitrate solution to obtain copper metal by a single-displacement reaction. From the known moles of copper nitrate in solution, she calculated the expected mass of copper metal as \(6.7 \mathrm{~g}\). When she weighed the copper on a balance, the mass was \(5.7 \mathrm{~g}\). (a) What is the actual yield of copper metal? (b) What is the theoretical yield of copper metal? (c) Calculate the percent yield.

Suppose you have a piece of aluminum that you want to react completely by the following single-displacement reaction: $$ 2 \mathrm{Al}(s)+6 \mathrm{HNO}_{3}(a q) \longrightarrow 2 \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}(a q)+3 \mathrm{H}_{2}(\mathrm{~g}) $$ (a) What mole ratio would you use in the following equation to determine the number of moles of \(\mathrm{HNO}_{3}\) needed to react with a known amount of Al? \(\operatorname{mol} \mathrm{Al} x\) \(=\mathrm{mol} \mathrm{HNO}_{3}\) (b) If you add more than enough nitric acid so that all the aluminum reacts, what mole ratio would you use in the following equation to determine the moles of \(\mathrm{H}_{2}\) produced? $$ \mathrm{mol} \mathrm{Al} \times==\mathrm{mol} \mathrm{H}_{2} $$ (c) Suppose you know the number of moles of \(\mathrm{H}_{2}\) product formed and you want to know the number of moles of Al that reacted. What mole ratio would you use in the following equation? $$ \mathrm{mol} \mathrm{H}_{2} \times \overline{\mathrm{mol}} \mathrm{Al} $$

The reaction that produces the water gas mixture, described in Question 6.99, is $$ \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g) $$ This reaction requires an input of \(131 \mathrm{~kJ}\) of heat for every mole of carbon that reacts. (a) Is this reaction endothermic or exothermic? (b) What is the energy change for this reaction in units of \(\mathrm{kJ} / \mathrm{mol}\) of carbon?

Ethanol, used in alcoholic beverages, can be produced by the fermentation of sucrose, which is found in sugar cane and other plants. The balanced equation for the fermentation process is $$ \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{\mathrm{n}}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}(l)+4 \mathrm{CO}_{2}(\mathrm{~g}) $$ (a) What mass of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}\), would be produced when \(2.50 \mathrm{~g}\) sucrose reacts by this process? (b) What mass of \(\mathrm{CO}_{2}\) would also be produced?
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