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Chapter 5: Problem 76

Calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with water to form acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and \(\mathrm{Ca}(\mathrm{OH})_{2}\). From the following enthalpy of reaction data and data in Appendix C, calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{CaC}_{2}(s);\) $$ \begin{aligned} \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g) & \\ \Delta H^{\circ}=&-127.2 \mathrm{~kJ} \end{aligned} $$

Short Answer

Expert verified
The enthalpy of formation for calcium carbide, \(\mathrm{CaC}_{2}(s)\), is \(-63.5\,\mathrm{kJ/mol}\).

Step by step solution

01

Write down the given reaction and enthalpy change

The given balanced chemical equation for the reaction of calcium carbide with water is: $$ \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g) $$The standard enthalpy change, \(\Delta H^{\circ}\), for this reaction is -127.2 kJ.
02

Write the general equation for standard enthalpy change

The general equation relating the standard enthalpy change of a reaction to the enthalpies of formation of the species involved is: $$ \Delta H^{\circ} = \sum n_i \Delta H_{f,i}^{\circ}(\text{products}) - \sum n_i \Delta H_{f,i}^{\circ}(\text{reactants}) $$
03

Find the standard enthalpies of formation for other species

We will find the values of \(\Delta H_{f}^{\circ}\) for the different species involved in the reaction from Appendix C or any standard thermodynamic data table. The values are: $$ \begin{aligned} \Delta H_{f}^{\circ}(\mathrm{H}_{2}\mathrm{O}(l)) &= -285.8\,\mathrm{kJ/mol} \\ \Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s)) &= -985.2\,\mathrm{kJ/mol} \\ \Delta H_{f}^{\circ}(\mathrm{C}_{2}\mathrm{H}_{2}(g)) &= 226.7\,\mathrm{kJ/mol} \\ \end{aligned} $$
04

Substitute the given data in the general equation

Substitute the given values and the values found in Step 3 into the general equation for \(\Delta H^{\circ}\): $$ \begin{aligned} -127.2\,\mathrm{kJ} &= \left[\Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s)) + \Delta H_{f}^{\circ}(\mathrm{C}_{2} \mathrm{H}_{2}(g))\right] - \left[\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) + 2 \Delta H_{f}^{\circ}(\mathrm{H}_{2}\mathrm{O}(l))\right] \end{aligned} $$
05

Solve for the enthalpy of formation of calcium carbide

Now, rearrange the equation and solve for \(\Delta H_{f}^{\circ}(\mathrm{CaC}_{2})\): $$ \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}) = \Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s)) + \Delta H_{f}^{\circ}(\mathrm{C}_{2} \mathrm{H}_{2}(g)) - 2 \Delta H_{f}^{\circ}(\mathrm{H}_{2}\mathrm{O}(l)) + 127.2\,\mathrm{kJ} $$Using the values from Step 3, we have: $$ \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}) = (-985.2\,\mathrm{kJ/mol}) + (226.7\,\mathrm{kJ/mol}) - 2(-285.8\,\mathrm{kJ/mol}) + 127.2\,\mathrm{kJ} $$Calculating the result: $$ \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}) = -63.5\,\mathrm{kJ/mol} $$ So, the enthalpy of formation for calcium carbide, \(\mathrm{CaC}_{2}(s)\), is \(-63.5\,\mathrm{kJ/mol}\).

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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}\( of each substance. \)(\mathbf{c})$ Which is the most efficient fuel in terms of heat evolved per unit mass?

Without doing any calculations, predict the sign of \(\Delta H\) for each of the following reactions: (a) $\mathrm{NaCl}(s) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{Cl}^{-}(\mathrm{g})$ (b) \(2 \mathrm{H}(g) \longrightarrow \mathrm{H}_{2}(g)\) (c) \(\mathrm{Na}(g) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{e}^{-}\) (d) \(\mathrm{I}_{2}(s) \longrightarrow \mathrm{I}_{2}(l)\)

A house is designed to have passive solar energy features. Brickwork incorporated into the interior of the house acts as a heat absorber. Each brick weighs approximately \(1.8 \mathrm{~kg}\). The specific heat of the brick is \(0.85 \mathrm{~J} / \mathrm{g}-\mathrm{K} .\) How many bricks must be incorporated into the interior of the house to provide the same total heat capacity as \(1.7 \times 10^{3}\) gal of water?

Two solid objects, A and B, are placed in boiling water and allowed to come to the temperature of the water. Each is then lifted out and placed in separate beakers containing \(1000 \mathrm{~g}\) of water at \(10.0^{\circ} \mathrm{C}\). Object A increases the water temperature by $3.50^{\circ} \mathrm{C} ; \mathrm{B}\( increases the water temperature by \)2.60{ }^{\circ} \mathrm{C}$. (a) Which object has the larger heat capacity? (b) What can you say about the specific heats of \(\mathrm{A}\) and \(\mathrm{B}\) ?

Consider two solutions, the first being \(50.0 \mathrm{~mL}\) of $1.00 \mathrm{M} \mathrm{CuSO}_{4}\( and the second \)50.0 \mathrm{~mL}\( of \)2.00 \mathrm{M} \mathrm{KOH} .$ When the two solutions are mixed in a constant-pressure calorimeter, a precipitate forms and the temperature of the mixture rises from 21.5 to \(27.7^{\circ} \mathrm{C} .(\mathbf{a})\) Before mixing, how many grams of Cu are present in the solution of \(\mathrm{CuSO}_{4}\) ? (b) Predict the identity of the precipitate in the reaction. (c) Write complete and net ionic equations for the reaction that occurs when the two solutions are mixed. \((\mathbf{d})\) From the calorimetric data, calculate \(\Delta H\) for the reaction that occurs on mixing. Assume that the calorimeter absorbs only a negligible quantity of heat, that the total volume of the solution is \(100.0 \mathrm{~mL},\) and that the specific heat and density of the solution after mixing are the same as those of pure water.
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