Problem 1
When a gas expands rapidly through a valve, you often feel the valve get colder. This is an adiabatic expansion \((q=0)\). Calculate the decrease in temperature of \(1.0\) mole of ideal gas as it is expanded from \(0.20\) to \(1.00\) liter under the conditions given below. Assume a constant volume molar heat capacity, \(C_{V}\) of \(\frac{3}{2} R\). Note that the energy, \(E\), of an ideal gas depends only on the temperature: It is independent of the volume of the system. A. The expansion is irreversible with an external pressure of 1 atmosphere and an initial temperature of \(300 \mathrm{~K}\), B. The expansion is reversible with an initial temperature of \(300 \mathrm{~K}\). C. Calculate \(\Delta E\) for the changes in state described in parts \(\mathrm{A}\) and \(\mathrm{B}\). D. Assume the expansion is carried out isothermally at \(300 \mathrm{~K}\), rather than adiabatically. Calculate the work done if the expansion is carried out irreversibly with an external pressure of \(1.0\) atmosphere. E. Calculate the work done if the isothermal expansion is carried out reversibly. F. Calculate \(q\) and \(\Delta E\) for the changes in state described in parts \(D\) and \(E\)
Problem 3
Calculate the enthalpy change for the oxidation of pyruvic acid to acetic acid under standard conditions. $$ 2 \mathrm{CH}_{3} \mathrm{COCOOH}(/)+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{CH}_{3} \mathrm{COOH}(/)+2 \mathrm{CO}_{2}(\mathrm{~g}) $$ The heats of combustion of pyruvic acid and acetic acid under standard conditions are \(-227 \mathrm{kcal} / \mathrm{mol}\) and \(-207 \mathrm{kcal} / \mathrm{mol}\), respectively. Heats of combustion are determined by reacting pyruvic or acetic acid with \(\mathrm{O}_{2}(\mathrm{~g})\) to give \(\mathrm{H}_{2} \mathrm{O}(/)\) and \(\mathrm{CO}_{2}\) (g). Hint: First write balanced chemical equations for the combustion processes.
Problem 4
Calculate the amount of water (in liters) that would have to be vaporized at \(40^{\circ} \mathrm{C}\) (approximately body temperature) to expend the \(2.5 \times 10^{6}\) calories of heat generated by a person in one day (commonly called sweating). The heat of vaporization of water at this temperature is \(574 \mathrm{cal} / \mathrm{g}\). We normally do not sweat that much. What's wrong with this calculation? If \(1 \%\) of the energy produced as heat could be utilized as mechanical work, how large a weight could be lifted I meter?
Problem 5
A. One hundred milliliters of \(0.200 \mathrm{M}\) ATP is mixed with an ATPase in a Dewar at \(298 \mathrm{~K}, 1\) atm, \(\mathrm{pH} 7.0, \mathrm{pMg} 3.0\), and \(0.25 \mathrm{M}\) ionic strength. The temperature of the solution increases \(1.48 \mathrm{~K}\). What is \(\Delta H^{*}\) for the hydrolysis of ATP to adenosine 5'-diphosphate (ADP) and phosphate? Assume the heat capacity of the system is \(418 \mathrm{~J} / \mathrm{K}\). B. The hydrolysis reaction can be written as $$ \mathrm{ATP}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{ADP}+\mathrm{P}_{\mathrm{i}} $$ Under the same conditions, the hydrolysis of ADP, $$ \mathrm{ADP}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{AMP}+\mathrm{P}_{\mathrm{i}} $$ has a heat of reaction, \(\Delta H^{\circ}\), of \(-28.9 \mathrm{~kJ} / \mathrm{mol}\). Under the same conditions, calculate \(\Delta H^{\circ}\) for the adenylate kinase reaction: $$ 2 \mathrm{ADP} \rightleftharpoons \mathrm{AMP}+\mathrm{ATP} $$
