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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 \(\mathrm{C},\) calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{CaC}_{2}(s) :\) $$\begin{aligned} \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \\ & \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \Delta H^{\circ}=-127.2 \mathrm{kJ} \end{aligned}$$

Short Answer

Expert verified
The standard enthalpy of formation for calcium carbide (CaC2) is approximately -1203 kJ/mol.

Step by step solution

01

Write down the enthalpy change for the reaction

We are given the enthalpy change of the reaction as: \[ \Delta H^{\circ} = -127.2~\mathrm{kJ} \]
02

Recall the formula for enthalpy change of a reaction

The enthalpy change of a reaction can be calculated using the following equation: \[ \Delta H^{\circ} = \sum \Delta H_{f}^{\circ}(\text{products}) - \sum \Delta H_{f}^{\circ}(\text{reactants}) \]
03

Write down the enthalpies of formation for the other substances

From Appendix C, we find the following standard enthalpies of formation: \begin{align*} \Delta H_{f}^{\circ}(\mathrm{H}_2\mathrm{O}(l)) &= -285.8~\mathrm{kJ/mol} \\ \Delta H_{f}^{\circ}(\mathrm{C}_{2}\mathrm{H}_{2}(g)) &= 226.7~\mathrm{kJ/mol} \\ \Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s)) &= -986.1~\mathrm{kJ/mol} \end{align*} We are looking for the standard enthalpy of formation for CaC2(s), which we will denote as 螖Hf掳(CaC2(s)).
04

Substitute the values into the formula

Now, we can substitute the given values into the formula for enthalpy change of the reaction: \begin{align*} -127.2~\text{kJ} &= [\Delta H_{f}^{\circ}(\mathrm{Ca}(\mathrm{OH})_{2}(s)) + \Delta H_{f}^{\circ}(\mathrm{C}_{2}\mathrm{H}_{2}(g))] - [\Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) + 2 \Delta H_{f}^{\circ}(\mathrm{H}_2\mathrm{O}(l))] \\ -127.2~\text{kJ} &= [-986.1 + 226.7 - 2(285.8)~\mathrm{kJ/mol} - \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s))] \\ \end{align*}
05

Solve for 螖Hf掳(CaC2(s))

Now, we will solve for the standard enthalpy of formation for CaC2(s): \begin{align*} \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) &= -986.1 + 226.7 - 2(285.8) + 127.2 \\ \Delta H_{f}^{\circ}(\mathrm{CaC}_{2}(s)) &= -1203~\mathrm{kJ/mol} \end{align*} The standard enthalpy of formation for calcium carbide (CaC2) is approximately -1203 kJ/mol.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calcium Carbide
Calcium carbide, chemically represented as \(\text{CaC}_2\), is an important compound used in various industrial applications. It is a grayish-black solid and known for its ability to react with water to produce acetylene \(\text{C}_2\text{H}_2\) which is a valuable gas in welding and chemical synthesis. This compound is prominent in industries such as metal cutting, lighting, and chemical manufacturing due to its efficient and explosive nature when reacting with water.
  • Calcium carbide was first discovered in the late 19th century and quickly became essential.
  • It is produced industrially by reacting lime and coke at high temperatures.
  • The reaction with water involves the formation of byproducts such as calcium hydroxide \(\text{Ca(OH)}_2\).
Understanding the properties and reactions of calcium carbide is crucial in the context of energy production and chemical manufacturing processes.
Enthalpy Change
Enthalpy change is a key concept in thermochemistry, which describes the amount of heat absorbed or released during a chemical reaction at constant pressure. It is typically expressed in kilojoules per mole (kJ/mol) and is denoted as \(\Delta H\). In many chemical reactions, knowing the enthalpy change helps in assessing the energy efficiency and feasibility of the process.
  • Enthalpy change can be exothermic (heat releasing) or endothermic (heat absorbing). An example is the -127.2 kJ given for the reaction involving calcium carbide, indicating an exothermic reaction.
  • It is crucial for calculating other thermodynamic properties like Gibbs free energy.
  • Understanding enthalpy change aids in energy balance calculations in industrial processes.
Therefore, mastering enthalpy change calculations helps in predicting whether a reaction will occur spontaneously.
Chemical Reactions
Chemical reactions are processes where reactants are transformed into products. These reactions entail bonds breaking and forming, leading to a transformation in the chemical structure. The reaction of calcium carbide with water is an excellent example. When calcium carbide \((\text{CaC}_2)\) reacts with water, it produces acetylene \((\text{C}_2\text{H}_2)\) and calcium hydroxide \((\text{Ca(OH)}_2)\).
  • This particular reaction is widely used in the commercial production of acetylene gas, which is useful in welding.
  • Chemical reactions can be classified based on how the substances interact, such as synthesis, decomposition, single-replacement, and double-replacement reactions.
  • The energy changes associated with reactions, like enthalpy change, are fundamental to comprehending these processes on an energetic level.
By observing chemical reactions, scientists can learn about various substances' properties and how they change under different conditions.
Thermochemistry
Thermochemistry focuses on the study of the energy changes accompanying chemical reactions and physical transformations. It integrates principles of both chemistry and thermodynamics, offering insights into reaction energetics.
  • Thermochemistry principles help in calculating important thermodynamic quantities such as enthalpy (\(\Delta H\)), entropy (\(\Delta S\)), and Gibbs free energy (\(\Delta G\)).
  • The study can predict the direction of chemical reactions and their energy needs.
  • It is essential for designing energy-efficient chemical processes in varied industries, including petrochemicals, food, and pharmaceuticals.
Thermochemistry provides the tools to calculate the energy output of reactions like the reaction between calcium carbide and water, helping engineers and scientists create more sustainable and efficient industrial processes.

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Most popular questions from this chapter

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at \(25.1^{\circ} \mathrm{C} .\) A \(121.0-\mathrm{g}\) block of copper metal is heated to \(100.4^{\circ} \mathrm{C}\) by putting it in a beaker of boiling water. The specific heat of \(\mathrm{Cu}(s)\) is \(0.385 \mathrm{J} / \mathrm{g}-\mathrm{K}\) . The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of \(30.1^{\circ} \mathrm{C}\) (a) Determine the amount of heat, in J, lost by the copper block. (b) Determine the amount of heat gained by the water. The specific heat of water is \(4.18 \mathrm{J} / \mathrm{g}-\mathrm{K}\) . (c) The difference between your answers for (a) and (b) is due to heat loss through the Styrofoam cups and the heat necessary to raise the temperature of the inner wall of the apparatus. The heat capacity of the calorimeter is the amount of heat necessary to raise the temperature of the apparatus (the cups and the stopper) by 1 K. Calculate the heat capacity of the calorimeter in J/K. (d)What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant- pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constant-pressure process, \(\Delta H=0 .\) What can you conclude about \(\Delta E, q,\) and \(w ?\)

Assume that the following reaction occurs at constant pressure: $$2 \mathrm{Al}(s)+3 \mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AlCl}_{3}(s)$$ (a) If you are given \(\Delta H\) for the reaction, what additional information do you need to determine \(\Delta E\) for the process? (b) Which quantity is larger for this reaction? (c) Explain your answer to part (b).

Using values from Appendix \(\mathrm{C}\) , calculate the standard enthalpy change for each of the following reactions: $$ \begin{array}{l}{\text { (a) } 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)} \\ {\text { (b) } \mathrm{Mg}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)} \\ {\text { (c) } \mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (d) } \mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)}\end{array} $$

Consider the combustion of liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}(l) :\) $$\begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H &=-726.5 \mathrm{kJ} \end{aligned}$$ (a) What is the enthalpy change for the reverse reaction? (b) Balance the forward reaction with whole-number coefficients. What is \(\Delta H\) for the reaction represented by this equation? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If the reaction were written to produce \(\mathrm{H}_{2} \mathrm{O}(g)\) instead of \(\mathrm{H}_{2} \mathrm{O}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.
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