Three hydrocarbons that contain four carbons are listed here, along with their standard enthalpies of formation: $$ \begin{array}{llc} \hline \text { Hydrocarbon } & \text { Formula } & \Delta H_{f}^{0}(\mathrm{~kJ} / \mathrm{mol}) \\ \hline \text { Butane } & \mathrm{C}_{4} \mathrm{H}_{10}(g) & -125 \\ \text { 1-Butene } & \mathrm{C}_{4} \mathrm{H}_{8}(g) & -1 \\ \text { 1-Butyne } & \mathrm{C}_{4} \mathrm{H}_{6}(g) & 165 \\ \hline \end{array} $$ (a) For each of these substances, calculate the molar enthalpy of combustion to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) (b) Calculate the fuel value, in \(\mathrm{kJ} / \mathrm{g}\), for each of these compounds. (c) For each hydrocarbon, determine the percentage of hydrogen by mass. (d) By comparing your answers for parts (b) and (c), propose a relationship between hydrogen content and fuel value in hydrocarbons.

Step by step solution

01

Combustion reaction equations

Write the balanced combustion reaction equations for each hydrocarbon. Butane: \(C_4H_{10}(g) + 13/2~O_2(g) \to 4~CO_2(g) + 5~H_2O(l)\) 1-Butene: \(C_4H_{8}(g) + 6~O_2(g) \to 4~CO_2(g) + 4~H_2O(l)\) 1-Butyne: \(C_4H_{6}(g) + 11/2~O_2(g) \to 4~CO_2(g) + 3~H_2O(l)\)

02

Calculate the enthalpy change for the combustion reactions

Use Hess's Law, which states that the overall enthalpy change of a reaction is the sum of the enthalpy changes of the individual steps. For each reaction, consider the formation of carbon dioxide, liquid water, and the initial hydrocarbon compound. Butane: \(\Delta H_{comb}^{0} = 4 \Delta H_{f}(CO_2) + 5 \Delta H_{f}(H_2O) - \Delta H_{f}(C_4H_{10})\) 1-Butene: \(\Delta H_{comb}^{0} = 4 \Delta H_{f}(CO_2) + 4 \Delta H_{f}(H_2O) - \Delta H_{f}(C_4H_{8})\) 1-Butyne: \(\Delta H_{comb}^{0} = 4 \Delta H_{f}(CO_2) + 3 \Delta H_{f}(H_2O) - \Delta H_{f}(C_4H_{6})\) Use the provided standard enthalpies of formation and known values for \(CO_2\) and \(H_2O\) (-393.5 kJ/mol for \(CO_2\) and -285.8 kJ/mol for \(H_2O\)) to calculate the enthalpy of combustion for each hydrocarbon. (b) Calculate the fuel value for each compound in kJ/g.

03

Calculate the molar mass for each hydrocarbon

To find the fuel value per gram, we need to divide the molar enthalpy of combustion by the molar mass of the hydrocarbon. Butane: \(M = 4 (12.01) + 10 (1.01) \approx 58.12~g/mol\) 1-Butene: \(M = 4 (12.01) + 8 (1.01) \approx 56.10~g/mol\) 1-Butyne: \(M = 4 (12.01) + 6 (1.01) \approx 54.08~g/mol\)

04

Calculate the fuel value

Divide the molar enthalpy of combustion (from step 2) by the molar mass (from step 3) to obtain the fuel value in kJ/g. (c) Determine the percentage of hydrogen by mass for each hydrocarbon.

05

Calculate the mass of hydrogen in each hydrocarbon

For each hydrocarbon, find the mass of hydrogen atoms and divide by the molar mass, multiplying by 100 to express it as a percentage. Butane: \(\frac{10 (1.01)}{58.12} × 100\%\) 1-Butene: \(\frac{8 (1.01)}{56.10} × 100\%\) 1-Butyne: \(\frac{6 (1.01)}{54.08} × 100\%\) (d) Propose a relationship between hydrogen content and fuel value in hydrocarbons.

06

Compare part (b) and part (c)

Compare the results from step 4 and step 5. Observe any trends or relationships between hydrogen content and fuel value for the hydrocarbons under examination.

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