Problem 37
A sheet of gold weighing \(10.0 \mathrm{~g}\) and at a temperature of \(18.0^{\circ} \mathrm{C}\) is placed flat on a sheet of iron weighing \(20.0 \mathrm{~g}\) and at a temperature of \(55.6^{\circ} \mathrm{C}\). What is the final temperature of the combined metals? Assume that no heat is lost to the surroundings.
Problem 38
A \(0.1375-\mathrm{g}\) sample of solid magnesium is burned in a constant-volume bomb calorimeter that has a heat capacity of \(3024 \mathrm{~J} /{ }^{\circ} \mathrm{C}\). The temperature increases by \(1.126^{\circ} \mathrm{C}\). Calculate the heat given off by the burning \(\mathrm{Mg},\) in \(\mathrm{kJ} / \mathrm{g}\) and in \(\mathrm{kJ} / \mathrm{mol} .\)
Problem 39
A quantity of \(2.00 \times 10^{2} \mathrm{~mL}\) of \(0.862 \mathrm{M} \mathrm{HCl}\) is mixed with \(2.00 \times 10^{2} \mathrm{~mL}\) of \(0.431 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the \(\mathrm{HCl}\) and \(\mathrm{Ba}(\mathrm{OH})_{2}\) solutions is the same at \(20.48^{\circ} \mathrm{C}\). For the process $$\mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)$$ the heat of neutralization is \(-56.2 \mathrm{~kJ} / \mathrm{mol}\). What is the final temperature of the mixed solution? Assume the specific heat of the solution is the same as that for pure water.
Problem 40
A \(50.75-\mathrm{g}\) sample of water at \(75.6^{\circ} \mathrm{C}\) is added to a sample of water at \(24.1^{\circ} \mathrm{C}\) in a constant-pressure calorimeter. If the final temperature of the combined water is \(39.4^{\circ} \mathrm{C}\) and the heat capacity of the calorimeter is \(26.3 \mathrm{~J} /{ }^{\circ} \mathrm{C},\) calculate the mass of the water originally in the calorimeter.
Problem 43
Consider two metals A and B, each having a mass of \(100 \mathrm{~g}\) and an initial temperature of \(20^{\circ} \mathrm{C}\). The specific heat of \(\mathrm{A}\) is larger than that of \(\mathrm{B}\). Under the same heating conditions, which metal would take longer to reach a temperature of \(21^{\circ} \mathrm{C} ?\)
Problem 44
Consider the following data:$$\begin{array}{lcc}\text { Metal } & \text { Al } & \text { Cu } \\\\\hline \text { Mass }(\mathrm{g}) & 10 & 30 \\\\\text { Specific heat }\left(\mathrm{J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) & 0.900 & 0.385 \\\\\text { Temnerature }{ }^{\circ}{ }^{\circ} \mathrm{C} \text { ) } & 40 & 60\end{array}$$ When these two metals are placed in contact, which of the following will take place? (a) Heat will flow from \(\mathrm{Al}\) to Cu because \(\mathrm{Al}\) has a larger specific heat. (b) Heat will flow from \(\mathrm{Cu}\) to \(\mathrm{Al}\) because \(\mathrm{Cu}\) has a larger mass. (c) Heat will flow from \(\mathrm{Cu}\) to \(\mathrm{Al}\) because \(\mathrm{Cu}\) has a larger heat capacity (d) Heat will flow from Cu to Al because Cu is at a higher temperature. (e) No heat will flow in either direction.
Problem 45
State Hess's law. Explain, with one example, the usefulness of Hess's law in thermochemistry.
Problem 46
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.
Problem 47
Given the thermochemical data,$$\begin{array}{ll}\mathrm{A}+6 \mathrm{~B} \longrightarrow 4 \mathrm{C} & \Delta H_{1}=-1200 \mathrm{~kJ} / \mathrm{mol} \\\\\mathrm{C}+\mathrm{B} \longrightarrow \mathrm{D} & \Delta H_{1}=-150 \mathrm{~kJ} / \mathrm{mol}\end{array}$$ Determine the enthalpy change for each of the following: a) \(\mathrm{D} \longrightarrow \mathrm{C}+\mathrm{B}\) d) \(2 \mathrm{D} \longrightarrow 2 \mathrm{C}+2 \mathrm{~B}\) b) \(2 \mathrm{C} \longrightarrow \frac{1}{2} \mathrm{~A}+3 \mathrm{~B}\) e) \(6 \mathrm{D}+\mathrm{A} \longrightarrow 10 \mathrm{C}\) c) \(3 \mathrm{D}+\frac{1}{2} \mathrm{~A} \stackrel{\longrightarrow}{\longrightarrow} \mathrm{C}\)
Problem 48
Given the thermochemical data, \(\mathrm{A}+\mathrm{B} \longrightarrow 2 \mathrm{C} \quad \Delta H_{1}=600 \mathrm{~kJ} / \mathrm{mol}\) \(\begin{array}{ll}2 \mathrm{C}+\mathrm{D} \longrightarrow 2 \mathrm{E} & \Delta H_{1}=210 \mathrm{~kJ} / \mathrm{mol}\end{array}\) Determine the enthalpy change for each of the following: a) \(4 \mathrm{E} \longrightarrow 4 \mathrm{C}+2 \mathrm{D}\) d) \(2 C+2 E \longrightarrow 2 A+2 B+D\) b) \(\mathrm{A}+\mathrm{B}+\mathrm{D} \longrightarrow 2 \mathrm{E}\) e) \(\mathrm{E} \longrightarrow \frac{1}{2} \mathrm{~A}+\frac{1}{2} \mathrm{~B}+\frac{1}{2} \mathrm{D}\) c) \(\mathrm{C} \longrightarrow \frac{1}{2} \mathrm{~A}+\frac{1}{2} \mathrm{~B}\)
