From the data in Table 5.2, determine which of the following fuels produces the greatest amount of heat per gram when burned under standard conditions: CO(g), CH4(g), or C2H2(g).

Short Answer

Expert verified

The greatest amount of heat per gram is produced by CO(g).

Step by step solution

01

Enthalpy of combustion

When a pure combustible substance is burned, it forms incombustible products like water and carbon dioxide, and the heat released during this process is termed enthalpy of combustion.

We have to calculate the enthalpy of combustion for each of these gases and then compare their values.

02

Amount of heat produced for CO (g)

\(\begin{array}{l}{\rm{Enthalpy of combustion of CO(g) is }} - 283.0{\rm{ kJ/mol}}{\rm{.}}\\{\rm{Here, we have been asked to calculate in per gram, }}\\{\rm{So, amount of heat per gram = }}1{\rm{ gm CO(g) }} \times \frac{{1{\rm{ mol CO(g)}}}}{{28.01{\rm{ gm CO(g)}}}} \times \frac{{ - 283.0{\rm{ kJ}}}}{{1{\rm{ mol CO(g)}}}}\\{\rm{ = }} - 10.10{\rm{ kJ/gram }}\end{array}\)

Hence, the amount of heat produced for CO(g) is -10.10 kJ/gram.

03

Amount of heat produced for CH4 (g)

\(\begin{array}{l}{\rm{Enthalpy of combustion of C}}{{\rm{H}}_4}{\rm{(g) is }} - 890.8{\rm{ kJ/mol}}{\rm{.}}\\{\rm{Here, we have been asked to calculate in per gram, }}\\{\rm{So, amount of heat per gram = }}1{\rm{ gm C}}{{\rm{H}}_4}{\rm{(g) }} \times \frac{{1{\rm{ mol C}}{{\rm{H}}_4}{\rm{(g)}}}}{{16.042{\rm{ gm C}}{{\rm{H}}_4}{\rm{(g)}}}} \times \frac{{ - 890.8{\rm{ kJ}}}}{{1{\rm{ mol C}}{{\rm{H}}_4}{\rm{(g)}}}}\\{\rm{ = }} - 55.53{\rm{ kJ/gram }}\end{array}\)

Hence, the amount of heat produced for \({\rm{C}}{{\rm{H}}_4}\)(g) will be -55.53 kJ/gram.

04

Amount of heat produced for C2H2 (g)

\(\begin{array}{l}{\rm{Enthalpy of combustion of }}{{\rm{C}}_2}{{\rm{H}}_2}{\rm{(g) is }} - 1301.1{\rm{ kJ/mol}}{\rm{.}}\\{\rm{Here, we have been asked to calculate in per gram, }}\\{\rm{So, amount of heat per gram = }}1{\rm{ gm }}{{\rm{C}}_2}{{\rm{H}}_2}{\rm{(g) }} \times \frac{{1{\rm{ mol }}{{\rm{C}}_2}{{\rm{H}}_2}{\rm{(g)}}}}{{{\rm{26}}{\rm{.035 gm }}{{\rm{C}}_2}{{\rm{H}}_2}{\rm{(g)}}}} \times \frac{{ - 1301.1{\rm{ kJ}}}}{{1{\rm{ mol }}{{\rm{C}}_2}{{\rm{H}}_2}{\rm{(g)}}}}\\{\rm{ = }} - 44.97{\rm{ kJ/gram }}\end{array}\)

Hence, the amount of heat produced for C2H2(g) will be -44.97 kJ/gram.

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Most popular questions from this chapter

Propane, \({{\bf{C}}_{\bf{3}}}{{\bf{H}}_{\bf{8}}}\), is a hydrocarbon that is commonly used as a fuel.

(a) Write a balanced equation for the complete combustion of propane gas.

(b) Calculate the volume of air at 25 °C and 1.00 atmosphere that is needed to completely combust 25.0 grams of propane. Assume that air is 21.0 percent O2 by volume. (Hint: we will see how to do this calculation in a later

chapter on gases—for now use the information that 1.00 L of air at 25 °C and 1.00 atm contains 0.275 g of O2 per liter.)

(c) The heat of combustion of propane is −2,219.2 kJ/mol. Calculate the heat of formation,ΔHf °of propane given thatΔHf °of H2O(l) = −285.8 kJ/mol andΔHf °of CO2(g) = −393.5 kJ/mol.

(d) Assuming that all of the heat released in burning 25.0 grams of propane is transferred to 4.00 kilograms of water, calculate the increase in temperature of the water.

From the molar heats of formation in Appendix G, determine how much heat is required to evaporate one mole of water:\({{\bf{H}}_{\bf{2}}}{\bf{O}}\left( {\bf{l}} \right) \to {{\bf{H}}_{\bf{2}}}{\bf{O}}\left( {\bf{g}} \right)\)

The white pigment \({\bf{Ti}}{{\bf{O}}_{\bf{2}}}\)is prepared by the reaction of titanium tetrachloride, \({\bf{TiC}}{{\bf{l}}_{\bf{4}}}\), with water vapor in the gas phase:

\({\bf{TiC}}{{\bf{l}}_{\bf{4}}}\left( {\bf{g}} \right){\bf{ + 2}}{{\bf{H}}_{\bf{2}}}{\bf{O}}\left( {\bf{g}} \right) \to {\bf{Ti}}{{\bf{O}}_{\bf{2}}}\left( {\bf{s}} \right){\bf{ + 4HCl}}\left( {\bf{g}} \right)\)

How much heat is evolved in the production of exactly 1 mole of \({\bf{Ti}}{{\bf{O}}_{\bf{2}}}\)(s) under standard state conditions?

Calculate the enthalpy of combustion of butane, C4H10(g) for the formation of H2O(g) and CO2(g). The enthalpy of formation of butane is -126 kJ/mol.

When a 3.00-g sample of KCl was added to 3.00×102 g of water in a coffee cup calorimeter, the temperature decreased by 1.05 °C. How much heat is involved in the dissolution of the KCl? What assumptions did you make?

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