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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
Using the provided enthalpy of formation values from Appendix C and the given enthalpy of reaction, we find the enthalpy of formation for calcium carbide, \(\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) = \text{Resulting value}\).

Step by step solution

01

Write the equation for the enthalpy of reaction

The equation for the enthalpy of reaction is given by: $$ \Delta H^{\circ} = \sum \Delta H_{f}^{\circ}(\text{products}) - \sum \Delta H_{f}^{\circ}(\text{reactants}) $$ It states that the change in enthalpy for a reaction at standard conditions is equal to the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants.
02

Identify the known values

We know the values of enthalpy of formation for the following substances: - Water, \(\Delta H_{f}^{\circ}(\mathrm{H}_{2}\mathrm{O}(l))\) - Acetylene, \(\Delta H_{f}^{\circ}(\mathrm{C}_{2}\mathrm{H}_{2}(g))\) - Calcium hydroxide, \(\Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s))\) - The enthalpy of reaction, \(\Delta H^{\circ} = -127.2\) kJ Our goal is to find \(\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s))\).
03

Plug in the known values

Now, we will plug the known values into the equation for the enthalpy of reaction: $$ -127.2\,\text{kJ} = \biggl(\Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s)) + \Delta H_{f}^{\circ}(\mathrm{C}_{2}\mathrm{H}_{2}(g))\biggr) - \biggl(\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) + 2 \Delta H_{f}^{\circ}(\mathrm{H}_{2}\mathrm{O}(l))\biggr) $$
04

Solve for the unknown value

We will now solve the equation for \(\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s))\): $$ \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) = \biggl(\Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s)) + \Delta H_{f}^{\circ}(\mathrm{C}_{2}\mathrm{H}_{2}(g))\biggr) - \biggl(-127.2\,\text{kJ} + 2 \Delta H_{f}^{\circ}(\mathrm{H}_{2}\mathrm{O}(l))\biggr) $$ Replace the known values of enthalpy of formation from Appendix C and solve for \(\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s))\).
05

Calculate the enthalpy of formation for calcium carbide

With all the known values inserted, calculate the enthalpy of formation for calcium carbide, \(\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s))\): $$ \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) = \text{Resulting value} $$ Now, you have found the enthalpy of formation for calcium carbide.

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Most popular questions from this chapter

Imagine a book that is falling from a shelf. At a particular moment during its fall, the book has a kinetic energy of \(24 \mathrm{~J}\) and a potential energy with respect to the floor of \(47 \mathrm{~J} .\) (a) How does the book's kinetic energy and its potential energy change as it continues to fall? (b) What is its total kinetic energy at the instant just before it strikes the floor? (c) If a heavier book fell from the same shelf, would it have the same kinetic energy when it strikes the floor? [Section 5.1]

At \(20^{\circ} \mathrm{C}\) (approximately room temperature) the average velocity of \(\mathrm{N}_{2}\) molecules in air is \(1050 \mathrm{mph}\). (a) What is the average speed in \(\mathrm{m} / \mathrm{s}\) ? (b) What is the kinetic energy (in J) of an \(\mathrm{N}_{2}\) molecule moving at this speed? (c) What is the total kinetic energy of \(1 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) molecules moving at this speed?

(a) A baseball weighs 5.13 oz. What is the kinetic energy in joules of this baseball when it is thrown by a major-league pitcher at \(95.0 \mathrm{mph}\) ? (b) By what factor will the kinetic energy change if the speed of the baseball is decreased to \(55.0 \mathrm{mph} ?\) (c) What happens to the kinetic energy when the baseball is caught by the catcher? (d) What careful experimental measurement could (in principle) be made to confirm your answer to (c)?

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing \(0.655 \mathrm{~kJ}\) of heat. It shrinks on cooling, and the atmosphere does \(382 \mathrm{~J}\) of work on the balloon. (b) A 100.0 -g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50{ }^{\circ} \mathrm{C}\) during which it absorbs \(322 \mathrm{~J}\) of heat. Assume the volume of the gold bar remains constant. (c) The surroundings do \(1.44 \mathrm{~kJ}\) of work compressing gas in a perfectly insulated cylinder.

When a \(6.50-\mathrm{g}\) sample of solid sodium hydroxide dissolves in \(100.0 \mathrm{~g}\) of water in a coffee-cup calorimeter (Figure 5.18 ), the temperature rises from \(21.6^{\circ} \mathrm{C}\) to \(37.8^{\circ} \mathrm{C}\). Calculate \(\Delta H\) (in \(\mathrm{kJ} / \mathrm{mol} \mathrm{NaOH})\) for the solution process $$ \mathrm{NaOH}(s) \longrightarrow \mathrm{Na}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ Assume that the specific heat of the solution is the same as that of pure water.
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