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Chapter 5: Problem 36

Suppose that the gas-phase reaction \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow\) 2 \(\mathrm{NO}_{2}(g)\) were carried out in a constant-volume container at constant temperature. (a) Would the measured heat change represent \(\Delta H\) or \(\Delta E ?\) (b) If there is a difference, which quantity is larger for this reaction? (c) Explain your answer to part (b).

Short Answer

Expert verified
(a) The measured heat change in a constant-volume container at constant temperature represents the internal energy change, ΔE. (b) In this specific reaction, ΔH and ΔE are equal as there is no difference between them. (c) Since the reaction is carried out in a constant-volume container at constant temperature, and the change in volume (ΔV) is zero, it results in enthalpy change (ΔH) being equal to internal energy change (ΔE). Therefore, neither ΔH nor ΔE is larger, as they are equal in this situation.

Step by step solution

01

(a) Identifying the Measured Heat Change

: The heat change measured in a constant-volume container is equivalent to the change in internal energy (ΔE) of the reaction. Therefore, in this case, the measured heat change would represent ΔE.
02

(b) Determining the Larger Quantity Between ΔH and ΔE

: The relationship between the enthalpy change (ΔH) and internal energy change (ΔE), at constant temperature, is given by: \[\Delta H = \Delta E + P\Delta V\] Where P is the pressure and ΔV is the change in volume. Since the volume is constant in this case, ΔV = 0, which means that ΔH = ΔE. Therefore, there is no difference between ΔH and ΔE in this reaction, and they are equal.
03

(c) Explaining the Answer to Part (b)

: Since the reaction is carried out in a constant-volume container at constant temperature, the change in volume (ΔV) is zero. This means that the enthalpy change (ΔH) is equal to the internal energy change (ΔE) for this reaction. As a result, neither ΔH nor ΔE is larger, as they are equal in this specific situation.

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Most popular questions from this chapter

The standard enthalpies of formation of gaseous propyne \(\left(\mathrm{C}_{3} \mathrm{H}_{4}\right),\) propylene \(\left(\mathrm{C}_{3} \mathrm{H}_{6}\right),\) and propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) are \(+185.4,+20.4,\) and \(-103.8 \mathrm{kJ} / \mathrm{mol}\) , respectively.(a) Calculate the heat evolved per mole on combustion of each substance to yield \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) (b) Calculate the heat evolved on combustion of 1 \(\mathrm{kg}\) of each substance. (c) Which is the most efficient fuel in terms of heat evolved per unit mass?

Using values from Appendix \(\mathrm{C}\) , calculate the standard enthalpy change for each of the following reactions: $$ \begin{array}{l}{\text { (a) } 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)} \\ {\text { (b) } \mathrm{Mg}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (c) } \mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } \mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)}\end{array} $$

Calculate \(\Delta E\) and determine whether the process is endothermic or exothermic for the following cases: (a) \(q=0.763 \mathrm{kJ}\) and \(w=-840 \mathrm{J} .\) (b) A system releases 66.1 \(\mathrm{kJ}\) of heat to its surroundings while the surroundings do 44.0 \(\mathrm{kJ}\) of work on the system.

A \(201-\) lb man decides to add to his exercise routine by walking up three flights of stairs \((45 \mathrm{ft}) 20\) times per day. He figures that the work required to increase his potential energy in this way will permit him to eat an extra order of French fries, at 245 Cal, without adding to his weight. Is he correct in this assumption?

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at \(25.1^{\circ} \mathrm{C} .\) A \(121.0-\mathrm{g}\) block of copper metal is heated to \(100.4^{\circ} \mathrm{C}\) by putting it in a beaker of boiling water. The specific heat of \(\mathrm{Cu}(s)\) is \(0.385 \mathrm{J} / \mathrm{g}-\mathrm{K}\) . The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of \(30.1^{\circ} \mathrm{C}\) (a) Determine the amount of heat, in J, lost by the copper block. (b) Determine the amount of heat gained by the water. The specific heat of water is \(4.18 \mathrm{J} / \mathrm{g}-\mathrm{K}\) . (c) The difference between your answers for (a) and (b) is due to heat loss through the Styrofoam cups and the heat necessary to raise the temperature of the inner wall of the apparatus. The heat capacity of the calorimeter is the amount of heat necessary to raise the temperature of the apparatus (the cups and the stopper) by 1 K. Calculate the heat capacity of the calorimeter in J/K. (d)What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?
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