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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 ΔHf°(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 ΔHf°(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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Most popular questions from this chapter

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.

From the enthalpies of reaction $$\begin{aligned} \mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{HF}(g) & \Delta H=-537 \mathrm{kJ} \\ \mathrm{C}(s)+2 \mathrm{F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g) & \Delta H=-680 \mathrm{kJ} \\ 2 \mathrm{C}(s)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g) & \Delta H=+52.3 \mathrm{kJ} \end{aligned}$$ calculate \(\Delta H\) for the reaction of ethylene with \(\mathrm{F}_{2} :\) $$\mathrm{C}_{2} \mathrm{H}_{4}(g)+6 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$$

(a) What are the units of molar heat capacity? (b) What are the units of specific heat? (c) If you know the specific heat of copper, what additional information do you need to calculate the heat capacity of a particular piece of copper pipe?

(a) What is meant by the term fuel value? (b) Which is a greater source of energy as food, 5 g of fat or 9 g of carbohydrate? (c) The metabolism of glucose produces \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l) .\) How does the human body expel these reaction products?

(a) Write an equation that expresses the first law of thermodynamics in terms of heat and work. (b) Under what conditions will the quantities q and w be negative numbers?
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