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Chapter 6: Problem 44

Describe how chemists use Hess's law to determine the \(\Delta H_{\mathrm{f}}^{\circ}\) of a compound by measuring its heat (enthalpy) of combustion.

Short Answer

Expert verified
Hess's law, which states that the overall enthalpy change of a reaction is the same, regardless of the path it takes, is used by chemists to determine the \(\Delta H_{f}^{\circ}\) of a compound. They achieve this by measuring its heat of combustion and using that information, along with the recognized heat of combustion of elements in their standard states, to establish a Hess's law cycle. This framework enables them to compute the \(\Delta H_{f}^{\circ}\) of the compound.

Step by step solution

01

Understanding Hess's Law

Hess's Law states that the total enthalpy change for a chemical reaction doesn't depend on the pathway it takes, but is the same regardless of how many steps the reaction happens in. This implies that if a chemical equation can be expressed as the sum of multiple other equations, the \(\Delta H\) for that equation is the sum of the \(\Delta H\)s of those equations.
02

Recognizing the standard enthalpy of formation

The standard enthalpy of formation \(\Delta H_{f}^{\circ}\) is a measure of the energy absorbed or released when one mole of a compound is created directly from its elements in their standard states. Natural elements in their standard states have a \(\Delta H_{f}^{\circ}\) of zero.
03

Understanding the combustion reaction

A combustion reaction involves the burning of a substance, usually in oxygen gas, which releases heat (exothermic process). Therefore, measuring the heat of combustion helps in determining the energy change that occurs when one mole of a substance burns in oxygen.
04

Applying Hess's law

To find the \(\Delta H_{\mathrm{f}}^{\circ}\) of a compound, write the combustion reaction for that compound, measure its heat of combustion, and then use Hess’s law to determine the \(\Delta H_{\mathrm{f}}^{\circ}\) for the compound. The heat of combustion of the elements in their standard states is used along with the combustion reaction of the compound to form a Hess's Law cycle, which allows for the calculation of the \(\Delta H_{\mathrm{f}}^{\circ}\) for the compound.

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Most popular questions from this chapter

From the following heats of combustion, $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-726.4 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-393.5 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H_{\mathrm{rxn}}^{\circ}=&-285.8 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ calculate the enthalpy of formation of methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) from its elements: \(\mathrm{C}\) (graphite) \(+2 \mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\)

A gas expands in volume from \(26.7 \mathrm{~mL}\) to \(89.3 \mathrm{~mL}\) at constant temperature. Calculate the work done (in joules) if the gas expands (a) against a vacuum, (b) against a constant pressure of \(1.5 \mathrm{~atm},\) and (c) against a constant pressure of 2.8 atm.

(a) For most efficient use, refrigerator freezer compartments should be fully packed with food. What is the thermochemical basis for this recommendation? (b) Starting at the same temperature, tea and coffee remain hot longer in a thermal flask than chicken noodle soup. Explain.

You are given the following data: $$ \begin{array}{c} \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{H}(g) \quad \Delta H^{\circ}=436.4 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{Br}_{2}(g) \longrightarrow 2 \mathrm{Br}(g) \quad \Delta H^{\circ}=192.5 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{H}_{2}(g)+\mathrm{Br}_{2}(g) \longrightarrow 2 \mathrm{HBr}(g) \\ \Delta H^{\circ}=-72.4 \mathrm{~kJ} / \mathrm{mol} \end{array} $$ Calculate \(\Delta H^{\circ}\) for the reaction $$ \mathrm{H}(g)+\operatorname{Br}(g) \longrightarrow \operatorname{HBr}(g) $$

Decomposition reactions are usually endothermic, whereas combination reactions are usually exothermic. Give a qualitative explanation for these trends.
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