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Chapter 7: Problem 134

The standard molar enthalpy of formation of \(\mathrm{CO}_{2}(\mathrm{g})\) is equal to (a) \(0 ;\) (b) the standard molar heat of combustion of graphite; (c) the sum of the standard molar enthalpies of formation of \(\mathrm{CO}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) (d) the standard molar heat of combustion of \(\mathrm{CO}(\mathrm{g})\)

Short Answer

Expert verified
The standard molar enthalpy of formation of \(\mathrm{CO}_{2}(\mathrm{g})\) is equal to the standard molar heat of combustion of graphite and the standard molar heat of combustion of \(\mathrm{CO}(\mathrm{g})\). Therefore, the correct options are (b) and (d).

Step by step solution

01

Checking the statement (a)

The \(\mathrm{CO}_{2}(\mathrm{g})\) is formed from elementary substances, namely \(\mathrm{C}(s-\mathrm{graphite})\) and \(\mathrm{O}_{2}(\mathrm{g})\). Hence, its molar enthalpy of formation would not be zero, therefore, option (a) is not correct.
02

Checking the statement (b)

The standard molar heat of combustion of graphite is equal to the heat released when one mole of graphite is fully combusted to form \(\mathrm{CO}_{2}(\mathrm{g})\), which is exactly the negative of the molar enthalpy of formation of \(\mathrm{CO}_{2}(\mathrm{g})\). So, option (b) is correct.
03

Checking the statement (c)

The standard molar enthalpy of formation of a substance is defined as the change in enthalpy when one mole of the substance is formed from its elements in their standard states, not the sum of the molar enthalpies of formation of the elements. Moreover, the enthalpy of formation of \(\mathrm{O}_{2}(\mathrm{g})\) is zero since it's in its standard state. So, option (c) is incorrect.
04

Checking the statement (d)

The standard molar heat of combustion of \(\mathrm{CO}(\mathrm{g})\) corresponds to the heat released when one mole of \(\mathrm{CO}(\mathrm{g})\) is fully combusted to form \(\mathrm{CO}_{2}(\mathrm{g})\), which is exactly the negative of the molar enthalpy of formation of \(\mathrm{CO}_{2}(\mathrm{g})\) from \(\mathrm{CO}(\mathrm{g})\) and \(\frac{1}{2}\mathrm{O}_{2}(\mathrm{g})\). Thus, option (d) is correct.

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Key Concepts

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

Enthalpy of Combustion
Enthalpy of combustion refers to the heat energy released when a substance completely reacts with oxygen under standard conditions. It is a particular example of an enthalpy change, where the reactants are typically in their standard states, and the combustion products are carbon dioxide and water for organic compounds.

More formally, it is the change in enthalpy when one mole of a substance burns completely in oxygen to form these stable products. In the case of graphite, which is a form of pure carbon, its enthalpy of combustion can be experimentally measured by burning one mole of graphite in excess oxygen to form carbon dioxide gas. The enthalpy of combustion is always negative since combustion is an exothermic process, releasing heat to the surroundings.

Practical Relevance

Understanding the enthalpy of combustion is crucial because it helps in calculating the energy content of fuels. Mathematicians and scientists calculate these values to determine how much energy various substances can release, which is essential for various applications like heating, automotive performance, and power generation.
Thermochemistry
Thermochemistry is the branch of chemistry that deals with the energy changes that occur during chemical reactions and physical transformations. It is the study of the relationships between chemical reactions and energy changes involving heat.

One of the fundamental concepts of thermochemistry is the first law of thermodynamics which states that energy cannot be created or destroyed, only transformed from one form to another. This principle allows chemists to calculate the heat absorbed or released during chemical reactions.

Key Aspects of Thermochemistry

In practice, thermochemists are interested in various measurements like the enthalpy changes in reactions, calorimetry (the measurement of heat transfer), and the heat capacity of substances. These concepts help in understanding the balance of energy in chemical processes, which is vital for industries ranging from pharmaceuticals to materials science.
Chemical Thermodynamics
Chemical thermodynamics is a subfield of thermodynamics that focuses on the interrelation of energy changes with chemical reactions. It combines the principles of thermodynamics with the concepts of chemistry to predict the direction and extent of chemical reactions.

Central to chemical thermodynamics is the concept of Gibbs free energy, which is a thermodynamic potential that can predict the favorability of reactions. When the Gibbs free energy of a system decreases, the reaction can proceed spontaneously under constant pressure and temperature.

Applications of Chemical Thermodynamics

This field is fundamental in all areas of chemistry, from understanding biological systems and processes to designing large-scale chemical plants. By applying the laws of thermodynamics, scientists can design processes that are more energy-efficient, safer, and sustainable.
Enthalpy Change
Enthalpy change is the measure of heat change in a system at constant pressure. It is a central concept in both thermochemistry and chemical thermodynamics. The symbol for enthalpy change is ∆H where a negative value indicates an exothermic process (releases heat to the surroundings) and a positive value indicates an endothermic process (absorbs heat from the surroundings).

Specific to the standard molar enthalpy of formation, it represents the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. This value is particularly important for chemists as it sets the 'zero point' for a chemical compound's enthalpy, allowing them to compare the enthalpies of various compounds.

Enthalpy Change in Reactions

In a reaction, the enthalpy change can be calculated by subtracting the enthalpy of the reactants from the enthalpy of the products. It provides a quantitative measure of the energy change during a chemical reaction, which is vital for processes like reaction design, energy production, and materials engineering.

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Most popular questions from this chapter

Care must be taken in preparing solutions of solutes that liberate heat on dissolving. The heat of solution of \(\mathrm{NaOH}\) is \(-44.5 \mathrm{kJ} / \mathrm{mol} \mathrm{NaOH} .\) To what maximum temperature may a sample of water, originally at \(21^{\circ} \mathrm{C},\) be raised in the preparation of \(500 \mathrm{mL}\) of \(7.0 \mathrm{M}\) NaOH? Assume the solution has a density of \(1.08 \mathrm{g} / \mathrm{mL}\) and specific heat of \(4.00 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1}\).

The standard heats of combustion \(\left(\Delta H^{\circ}\right)\) per mole of 1,3-butadiene, \(\mathrm{C}_{4} \mathrm{H}_{6}(\mathrm{g}) ;\) butane, \(\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}) ;\) and \(\mathrm{H}_{2}(\mathrm{g})\) are \(-2540.2,-2877.6,\) and \(-285.8 \mathrm{kJ},\) respectively. Use these data to calculate the heat of hydrogenation of 1,3-butadiene to butane. $$\mathrm{C}_{4} \mathrm{H}_{6}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}) \quad \Delta H^{\circ}=?$$ [Hint: Write equations for the combustion reactions. In each combustion, the products are \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\left.\mathrm{H}_{2} \mathrm{O}(1) .\right]\)

In the Are You Wondering \(7-1\) box, the temperature variation of enthalpy is discussed, and the equation \(q_{P}=\) heat capacity \(\times\) temperature change \(=C_{P} \times \Delta T\) was introduced to show how enthalpy changes with temperature for a constant-pressure process. Strictly speaking, the heat capacity of a substance at constant pressure is the slope of the line representing the variation of enthalpy (H) with temperature, that is $$C_{P}=\frac{d H}{d T} \quad(\text { at constant pressure })$$ where \(C_{P}\) is the heat capacity of the substance in question. Heat capacity is an extensive quantity and heat capacities are usually quoted as molar heat capacities \(C_{P, \mathrm{m}},\) the heat capacity of one mole of substance; an intensive property. The heat capacity at constant pressure is used to estimate the change in enthalpy due to a change in temperature. For infinitesimal changes in temperature, $$d H=C_{p} d T \quad(\text { at constant pressure })$$ To evaluate the change in enthalpy for a particular temperature change, from \(T_{1}\) to \(T_{2}\), we write $$\int_{H\left(T_{1}\right)}^{H\left(T_{2}\right)} d H=H\left(T_{2}\right)-H\left(T_{1}\right)=\int_{T_{1}}^{T_{2}} C_{P} d T$$ If we assume that \(C_{P}\) is independent of temperature, then we recover equation (7.5) $$\Delta H=C_{P} \times \Delta T$$ On the other hand, we often find that the heat capacity is a function of temperature; a convenient empirical expression is $$C_{P, \mathrm{m}}=a+b T+\frac{c}{T^{2}}$$ What is the change in molar enthalpy of \(\mathrm{N}_{2}\) when it is heated from \(25.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C} ?\) The molar heat capacity of nitrogen is given by$$C_{P, \mathrm{m}}=28.58+3.77 \times 10^{-3} T-\frac{0.5 \times 10^{5}}{T^{2}} \mathrm{JK}^{-1} \mathrm{mol}^{-1}$$

A 465 g chunk of iron is removed from an oven and plunged into \(375 \mathrm{g}\) water in an insulated container. The temperature of the water increases from 26 to \(87^{\circ} \mathrm{C}\). If the specific heat of iron is \(0.449 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1},\) what must have been the original temperature of the iron?

The enthalpy of sublimation ( solid \(\rightarrow\) gas) for dry ice (i.e., \(\mathrm{CO}_{2}\) ) is \(\Delta H_{\mathrm{sub}}^{\circ}=571 \mathrm{kJ} / \mathrm{kg}\) at \(-78.5^{\circ} \mathrm{C} .\) If \(125.0 \mathrm{J}\) of heat is transferred to a block of dry ice that is \(-78.5^{\circ} \mathrm{C},\) what volume of \(\mathrm{CO}_{2} \operatorname{gas}(d=1.98 \mathrm{g} / \mathrm{L})\) will be generated?
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