Chapter 7: Problem 144
Construct a concept map encompassing the ideas behind the first law of thermodynamics.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 7: Problem 144
Construct a concept map encompassing the ideas behind the first law of thermodynamics.
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeIn each of the following processes, is any work done when the reaction is carried out at constant pressure in a vessel open to the atmosphere? If so, is work done by the reacting system or on it? (a) Neutralization of \(\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq})\) by \(\mathrm{HCl}(\mathrm{aq}) ;\) (b) conversion of gaseous nitrogen dioxide to gaseous dinitrogen tetroxide; (c) decomposition of calcium carbonate to calcium oxide and carbon dioxide gas.
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 plausible final temperature when \(75.0 \mathrm{mL}\) of water at \(80.0^{\circ} \mathrm{C}\) is added to \(100.0 \mathrm{mL}\) of water at \(20^{\circ} \mathrm{C}\) is (a) \(28^{\circ} \mathrm{C} ;\) (b) \(40^{\circ} \mathrm{C} ;\) (c) \(46^{\circ} \mathrm{C} ;\) (d) \(50^{\circ} \mathrm{C}\)
Construct a concept map to show the interrelationships between path-dependent and pathindependent quantities in thermodynamics.
The heat of neutralization of \(\mathrm{HCl}(\text { aq) by } \mathrm{NaOH}(\mathrm{aq})\) is \(-55.84 \mathrm{kJ} / \mathrm{mol} \mathrm{H}_{2} \mathrm{O}\) produced. If \(50.00 \mathrm{mL}\) of \(1.05 \mathrm{M}\) \(\mathrm{NaOH}\) is added to \(25.00 \mathrm{mL}\) of \(1.86 \mathrm{M} \mathrm{HCl}\), with both solutions originally at \(24.72^{\circ} \mathrm{C},\) what will be the final solution temperature? (Assume that no heat is lost to the surrounding air and that the solution produced in the neutralization reaction has a density of \(1.02 \mathrm{g} / \mathrm{mL}\) and a specific heat of \(3.98 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1}\).
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