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Chapter 6: Problem 86

The standard enthalpy of combustion of ethene gas, \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\), is \(-1411.1 \mathrm{~kJ} / \mathrm{mol}\) at \(298 \mathrm{~K}\). Given the following enthalpies of formation, calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})\). $$ \begin{array}{ll} \mathrm{CO}_{2}(g) & -393.5 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{H}_{2} \mathrm{O}(l) & -285.8 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

Short Answer

Expert verified
The standard enthalpy of formation for ethene gas \(\mathrm{C}_{2}\mathrm{H}_{4}(\mathrm{~g})\) is \(52.5~kJ/mol\).

Step by step solution

01

Write the balanced combustion reaction for ethene gas

The balanced combustion reaction for ethene gas can be written as follows: \[ C_2H_4(g) + 3O_2(g) \rightarrow 2CO_2(g) + 2H_2O(l) \] Here, ethene gas reacts with oxygen gas to form carbon dioxide and water.
02

Write the enthalpy change equation for the reaction

From Hess's Law, we know that the enthalpy change for the overall reaction is the sum of the enthalpy changes of all the individual components in the reaction. The equation for this reaction can be written as: \[ ΔH_{comb} = 2ΔH_{f}^{∘}(CO_2) + 2ΔH_{f}^{∘}(H_2O) - ΔH_{f}^{∘}(C_2H_4) - 3ΔH_{f}^{∘}(O_2) \] Since the standard enthalpy of formation of an element in its standard state is zero: \(ΔH_{f}^{∘}(O_2) = 0\) Therefore, the equation becomes: \[ ΔH_{comb} = 2ΔH_{f}^{∘}(CO_2) + 2ΔH_{f}^{∘}(H_2O) - ΔH_{f}^{∘}(C_2H_4) \]
03

Substitute the given values and solve for ΔHf°(C2H4)

We are given: - \( ΔH_{comb}(C_2H_4) = -1411.1~kJ/mol \) - \( ΔH_{f}^{∘}(CO_2) = -393.5~kJ/mol \) - \( ΔH_{f}^{∘}(H_2O) = -285.8~kJ/mol \) Substituting these values into the equation, we get: \[ -1411.1 = 2(-393.5) + 2(-285.8) - ΔH_{f}^{∘}(C_2H_4) \] Now, solve for \(\Delta H_{f}^{∘}(C_2H_4)\): \[ -1411.1 = -787 - 571.6 - ΔH_{f}^{∘}(C_2H_4) \] \[ -1411.1 = -1358.6 - ΔH_{f}^{∘}(C_2H_4) \] \[ ΔH_{f}^{∘}(C_2H_4) = -1358.6 + 1411.1 \] \[ ΔH_{f}^{∘}(C_2H_4) = 52.5~kJ/mol \] So, the standard enthalpy of formation for ethene gas \(\mathrm{C}_{2}\mathrm{H}_{4}(\mathrm{~g})\) is \(52.5~kJ/mol\).

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Most popular questions from this chapter

A coffee-cup calorimeter initially contains \(125 \mathrm{~g}\) water at \(24.2^{\circ} \mathrm{C}\). Potassium bromide \((10.5 \mathrm{~g})\), also at \(24.2^{\circ} \mathrm{C}\), is added to the water, and after the KBr dissolves, the final temperature is \(21.1^{\circ} \mathrm{C}\). Calculate the enthalpy change for dissolving the salt in \(\mathrm{J} / \mathrm{g}\) and \(\mathrm{kJ} / \mathrm{mol}\). Assume that the specific heat capacity of the solution is \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) and that no heat is transferred to the surroundings or to the calorimeter.

The enthalpy change for a reaction is a state function and it is an extensive property. Explain.

The preparation of \(\mathrm{NO}_{2}(g)\) from \(\mathrm{N}_{2}(g)\) and \(\mathrm{O}_{2}(g)\) is an endothermic reaction: $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) \text { (unbalanced) } $$ The enthalpy change of reaction for the balanced equation (with lowest whole- number coefficients) is \(\Delta H=67.7 \mathrm{~kJ}\). If \(2.50 \times 10^{2} \mathrm{~mL} \mathrm{~N}_{2}(g)\) at \(100 .{ }^{\circ} \mathrm{C}\) and \(3.50 \mathrm{~atm}\) and \(4.50 \times\) \(10^{2} \mathrm{~mL} \mathrm{O}_{2}(g)\) at \(100 .{ }^{\circ} \mathrm{C}\) and \(3.50\) atm are mixed, what amount of heat is necessary to synthesize the maximum yield of \(\mathrm{NO}_{2}(g) ?\)

The best solar panels currently available are about \(19 \%\) efficient in converting sunlight to electricity. A typical home will use about \(40 . \mathrm{kWh}\) of electricity per day \((1 \mathrm{kWh}=1 \mathrm{kilowatt}\) hour; \(1 \mathrm{~kW}=1000 \mathrm{~J} / \mathrm{s}\) ). Assuming \(8.0\) hours of useful sunlight per day, calculate the minimum solar panel surface area necessary to provide all of a typical home's electricity. (See Exercise 126 for the energy rate supplied by the sun.)

Are the following processes exothermic or endothermic? a. the combustion of gasoline in a car engine b. water condensing on a cold pipe c. \(\mathrm{CO}_{2}(s) \longrightarrow \mathrm{CO}_{2}(g)\) d. \(\mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{~F}(g)\)
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