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Chapter 5: Problem 42

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) \(1 \mathrm{~mol} \mathrm{I}_{2}(s)\) or $1 \mathrm{~mol} \mathrm{I}_{2}(g)$ at the same temperature, (b) \(2 \mathrm{~mol}\) of iodine atoms or \(1 \mathrm{~mol}\) of \(\mathrm{I}_{2},(\mathbf{c}) 1 \mathrm{~mol} \mathrm{I}_{2}(g)\) and $1 \mathrm{~mol} \mathrm{H}_{2}(g)$ at \(25^{\circ} \mathrm{C}\) or \(2 \mathrm{~mol} \mathrm{HI}(g)\) at $25^{\circ} \mathrm{C},(\mathbf{d}) 1 \mathrm{~mol} \mathrm{H}_{2}(g)\( at \)100^{\circ} \mathrm{C}$ or \(1 \mathrm{~mol} \mathrm{H}_{2}(g)\) at \(300^{\circ} \mathrm{C}\).

Short Answer

Expert verified
In summary, the substances or states with higher enthalpy in each case are: a) 1 mol of gaseous iodine (I₂) has a higher enthalpy than 1 mol of solid iodine (I₂) at the same temperature. b) 2 mol of iodine atoms have a higher enthalpy compared to 1 mol of I₂. c) The reactants (1 mol of I₂ gas and 1 mol of H₂ gas) have a higher enthalpy compared to the products (2 mol of HI gas) at 25°C. d) 1 mol of H₂ gas at 300°C has a higher enthalpy compared to 1 mol of H₂ gas at 100°C.

Step by step solution

01

Compare the phases of iodine

Since we are comparing 1 mol of solid iodine (I2) and 1 mol of gaseous iodine (I2) at the same temperature, we must consider the enthalpy change required to turn the solid iodine into a gas, known as enthalpy of sublimation or the enthalpy of the phase transition.
02

Predict which state of iodine has a higher enthalpy

It requires energy to convert solid iodine to gaseous iodine. This energy input increases the enthalpy of the system. Therefore, we can predict that 1 mol of gaseous iodine (I2) will have a higher enthalpy compared to 1 mol of solid iodine (I2) at the same temperature. #b) Comparing enthalpy of 2 mol of iodine atoms and 1 mol of iodine molecules#
03

Consider the bond dissociation energy

In order to compare the enthalpy of 2 mol of iodine atoms and 1 mol of I2 molecules, we need to consider the bond dissociation energy. Breaking the bond between two iodine atoms in an I2 molecule requires energy, which increases the enthalpy of the system.
04

Predict which has a higher enthalpy

Since it requires energy to break the bond between two iodine atoms in an I2 molecule, we can predict that having 2 mol of iodine atoms will have a higher enthalpy compared to 1 mol of I2. #c) Comparing enthalpy of 1 mol of I2 gas, 1 mol of H2 gas, and 2 mol of HI gas at 25°C#
05

Compare enthalpy of formation

In this case, we need to compare the enthalpy of the reactants to the enthalpy of the products at the given temperature. The reaction we are considering is: \[\mathrm{I}_{2}(g) + \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{HI}(g)\]
06

Predict which has a higher enthalpy

Since the formation of new bonds releases energy, the reactants must have a higher enthalpy than the products to provide energy for bond formation. We can predict that the reactants (1 mol of I2 gas and 1 mol of H2 gas) will have a higher enthalpy compared to the products (2 mol of HI gas) at 25°C. #d) Comparing enthalpy of 1 mol of H2 gas at 100°C and 1 mol of H2 gas at 300°C#
07

Understand the effect of temperature on enthalpy

Enthalpy is a state function and it increases with increasing temperature. In this case, we must compare the enthalpy of the same substance (H2 gas) at two different temperatures (100°C and 300°C).
08

Predict which has a higher enthalpy

Since enthalpy increases with increasing temperature, we can predict that 1 mol of H2 gas at 300°C will have a higher enthalpy compared to 1 mol of H2 gas at 100°C.

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Most popular questions from this chapter

An aluminum can of a soft drink is placed in a freezer. Later, you find that the can is split open and its contents have frozen. Work was done on the can in splitting it open. Where did the energy for this work come from?

(a) Derive an equation to convert the specific heat of a pure substance to its molar heat capacity. (b) The specific heat of aluminum is $0.9 \mathrm{~J} /(\mathrm{g} \cdot \mathrm{K}) .$ Calculate its molar heat capacity. (c) If you know the specific heat of aluminum, what additional information do you need to calculate the heat capacity of a particular piece of an aluminum component?

Consider the following reaction: $$ 2 \mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \quad \Delta H=+252.8 \mathrm{~kJ} $$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when \(24.0 \mathrm{~g}\) of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) is decomposed by this reaction at constant pressure. (c) For a given sample of \(\mathrm{CH}_{3} \mathrm{OH},\) the enthalpy change during the reaction is \(82.1 \mathrm{~kJ}\). How many grams of methane gas are produced? (d) How many kilojoules of heat are released when \(38.5 \mathrm{~g}\) of \(\mathrm{CH}_{4}(g)\) reacts completely with \(\mathrm{O}_{2}(g)\) to form \(\mathrm{CH}_{3} \mathrm{OH}(g)\) at constant pressure?

The decomposition of sodium bicarbonate (baking soda), \(\mathrm{NaHCO}_{3}(s)\), into $\mathrm{Na}_{2} \mathrm{CO}_{3}(s), \mathrm{H}_{2} \mathrm{O}(l)\(, and \)\mathrm{CO}_{2}(g)$ at constant pressure requires the addition of \(85 \mathrm{~kJ}\) of heat per two moles of \(\mathrm{NaHCO}_{3} .\) (a) Write a balanced thermochemical equation for the reaction. (b) Draw an enthalpy diagram for the reaction.

The gas-phase reaction shown, between \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), was run in an apparatus designed to maintain a constant pressure. (a) Write a balanced chemical equation for the reaction depicted and predict whether \(w\) is positive, negative, or zero. (b) Using data from Appendix C, determine \(\Delta H\) for the formation of one mole of the product. [Sections 5.3 and 5.7\(]\)
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