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Calculate \(\Delta H^{\circ}\) for the process \(\mathrm{Sb}(s)+\frac{5}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SbCl}_{5}(s)\) from the following information: \(\mathrm{Sb}(s)+\frac{3}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SbCl}_{3}(s) \quad \Delta H^{\circ}=-314 \mathrm{kJ}\) \(\mathrm{SbCl}_{3}(s)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SbCl}_{5}(s) \quad \Delta H^{\circ}=-80 \mathrm{kJ}\)

Short Answer

Expert verified
\( \Delta H^{\circ}_{\text{total}} = -394 \mathrm{kJ} \)

Step by step solution

01

Write down the enthalpy changes for the given reactions

First, recognize the enthalpy changes given for the reactions: For the process \(\mathrm{Sb}(s) + \frac{3}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SbCl}_{3}(s)\), the enthalpy change is \(-314 \mathrm{kJ}\). For the reaction \(\mathrm{SbCl}_{3}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SbCl}_{5}(s)\), the enthalpy change is \(-80 \mathrm{kJ}\).
02

Combine the reactions to form the desired process

To find the enthalpy change for the desired process \(\mathrm{Sb}(s) + \frac{5}{2} \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SbCl}_{5}(s)\), combine the two given reactions by adding them together. Since the second reaction forms \(\mathrm{SbCl}_{5}(s)\) from \(\mathrm{SbCl}_{3}(s)\) and an additional mole of \(\mathrm{Cl}_{2}(g)\), simply add it to the first reaction.
03

Calculate the overall enthalpy change

Add the enthalpy changes of the individual reactions to find the total enthalpy change for the desired process: \(-314 \mathrm{kJ}\) for the first reaction and \(-80 \mathrm{kJ}\) for the second reaction. \[\Delta H^{\circ}_{\text{total}} = \Delta H^{\circ}_{1} + \Delta H^{\circ}_{2} = (-314 \mathrm{kJ}) + (-80 \mathrm{kJ})\]

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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 associated with chemical reactions and physical transformations. It's a fundamental concept within thermodynamics that fisuses on how energy is transferred in the form of heat, particularly during chemical processes. When substances react chemically, they either absorb or release energy, often in the form of heat.

Understanding the heat involved in these reactions is crucial for predicting reaction behavior and for applications in various fields, including the design of energy-efficient processes in industries. This branch of chemistry uses principles such as conservation of energy and the quantitative relationship between heat and work.
Hess's Law
Hess's Law, named after Russian chemist Germain Hess, states that the total enthalpy change for a chemical reaction is the same, regardless of the number of steps the reaction is carried out in. This law is a direct consequence of enthalpy being a state function.

Hess's Law in Practice:

When you cannot measure the enthalpy change of a reaction directly, you can use Hess's Law to calculate it indirectly. This is done by adding the enthalpy changes of individual steps that lead from reactants to products. It's akin to taking different routes to reach the same destination. The total distance traveled (enthalpy change) will remain constant irrespective of the path taken.
Enthalpy Change
Enthalpy change, denoted as \(\Delta H\), is the measure of heat change during a process at constant pressure. It's an extensive property, meaning it depends on the substance's mass. The sign of \(\Delta H\) indicates whether the system absorbed heat (positive \(\Delta H\)) from the surroundings or released heat (negative \(\Delta H\)) to the surroundings.

Determining Enthalpy Change:

To figure out the enthalpy change for a reaction, one can either measure it experimentally through calorimetry or calculate it using Hess's Law and standard enthalpies of formation. It's an essential factor in determining the energy efficiency of chemical processes and the favorability of reactions.
Chemical Reactions
Chemical reactions involve the transformation of one set of chemical substances to another through the breaking and forming of chemical bonds. They are described by chemical equations that show the reactants transforming into products. Several factors such as temperature, pressure, and concentration affect how reactions proceed.

The study of chemical reactions encompasses understanding reaction mechanisms, rates, and equilibrium. Furthermore, energy changes that occur during reactions are a focal point in chemical thermodynamics, helping to elucidate why certain reactions happen and others don’t. Mastering the concepts behind chemical reactions is pivotal for predicting reaction outcomes and manipulation in practical applications.

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Most popular questions from this chapter

During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 kWh of heat provided by a natural gas furnace with \(89 \%\) efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house). (a) Assume that natural gas is pure methane and determine the volume of natural gas in cubic feet that was required to heat the house. The average temperature of the natural gas was \(56^{\circ} \mathrm{F} ;\) at this temperature and a pressure of \(1 \mathrm{atm}\) natural gas has a density of 0.681 g/L. (b) How many gallons of LPG (liquefied petroleum gas) would be required to replace the natural gas used? Assume the LPG is liquid propane \(\left[\mathrm{C}_{3} \mathrm{H}_{8}:\right.\) density, \(0.5318 \mathrm{g} / \mathrm{mL}\); enthalpy of combustion, \(2219 \mathrm{kJ} / \mathrm{mol}\) for the formation of \(\left.\mathrm{CO}_{2}(g) \text { and } \mathrm{H}_{2} \mathrm{O}(l)\right]\) and the furnace used to burn the LPG has the same efficiency as the gas furnace. (c) What mass of carbon dioxide is produced by combustion of the methane used to heat the house? (d) What mass of water is produced by combustion of the methane used to heat the house? (e) What volume of air is required to provide the oxygen for the combustion of the methane used to heat the house? Air contains \(23 \%\) oxygen by mass. The average density of air during the month was \(1.22 \mathrm{g} / \mathrm{L}\). (f) How many kilowatt-hours \(\left(1 \mathrm{kWh}=3.6 \times 10^{6} \mathrm{J}\right)\) of electricity would be required to provide the heat necessary to heat the house? Note electricity is \(100 \%\) efficient in producing heat inside a house. (g) Although electricity is 100\% efficient in producing heat inside a house, production and distribution of electricity is not \(100 \%\) efficient. The efficiency of production and distribution of electricity produced in a coal- fired power plant is about 40\%. A certain type of coal provides 2.26 kWh per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation and distribution is 40\%?

Propane, \(C_{3} \mathrm{H}_{8}\), is a hydrocarbon that is commonly used as a fuel. (a) Write a balanced equation for the complete combustion of propane gas. (b) Calculate the volume of air at \(25^{\circ} \mathrm{C}\) and 1.00 atmosphere that is needed to completely combust 25.0 grams of propane. Assume that air is 21.0 percent \(\mathrm{O}_{2}\) by volume. (Hint: We will see how to do this calculation in a later chapter on gases - for now use the information that \(1.00 \mathrm{L}\) of air at \(25^{\circ} \mathrm{C}\) and 1.00 atm contains \(0.275 \mathrm{g}\) of \(\mathrm{O}_{2}\) per liter.) (c) The heat of combustion of propane is \(-2,219.2 \mathrm{kJ} / \mathrm{mol}\). Calculate the heat of formation, \(\Delta H_{\mathrm{f}}^{\circ}\) of propane given that \(\Delta H_{\mathrm{f}}^{\circ} \quad\) of \(\mathrm{H}_{2} \mathrm{O}(l)=-285.8 \mathrm{kJ} / \mathrm{mol}\) and \(\Delta H_{\mathrm{f}}^{\circ} \quad\) of \(\mathrm{CO}_{2}(g)=-393.5 \mathrm{kJ} / \mathrm{mol}\) (d) Assuming that all of the heat released in burning 25.0 grams of propane is transferred to 4.00 kilograms of water, calculate the increase in temperature of the water.

Which compound in each of the following pairs has the larger lattice energy? Note: \(\mathrm{Ba}^{2+}\) and K 'have similar radii; S^- and Cl- have similar radii. Explain your choices. (a) \(\mathrm{K}_{2} \mathrm{O}\) or \(\mathrm{Na}_{2} \mathrm{O}\) (b) \(\mathrm{K}_{2} \mathrm{S}\) or \(\mathrm{BaS}\) (c) KCl or BaS (d) BaS or BaCl_

A 0.500-g sample of KCl is added to 50.0 g of water in a calorimeter (Figure 9.12). If the temperature decreases by \(1.05^{\circ} \mathrm{C},\) what is the approximate amount of heat involved in the dissolution of the \(\mathrm{KCl}\), assuming the specific heat of the resulting solution is \(4.18 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C}\) ? Is the reaction exothermic or endothermic?

Calculate \(\Delta H\) for the process \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{Cl}_{2}(g)\) from the following information: \(\mathrm{Hg}(l)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{HgCl}_{2}(s) \quad \Delta H=-224 \mathrm{kJ}\) \(\mathrm{Hg}(l)+\mathrm{HgCl}_{2}(s) \longrightarrow \mathrm{Hg}_{2} \mathrm{Cl}_{2}(s) \quad \Delta H=-41.2 \mathrm{kJ}\)

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