5.2 First law of thermodynamics and enthalpy  (Page 13/25)

In the early days of automobiles, illumination at night was provided by burning acetylene, C ₂ H ₂ . Though no longer used as auto headlamps, acetylene is still used as a source of light by some cave explorers. The acetylene is (was) prepared in the lamp by the reaction of water with calcium carbide, CaC ₂ :
${\text{CaC}}_2(s)+{\text{H}}_2\text{O}\left(l\right)⟶\text{Ca}{\left(\text{OH}\right)}_2(s)+{\text{C}}_2{\text{H}}_2(g).$
Calculate the standard enthalpy of the reaction. The $\text{Δ}{H}_{\text{f}}^{°}$ of CaC ₂ is −15.14 kcal/mol.

From the data in [link] , determine which of the following fuels produces the greatest amount of heat per gram when burned under standard conditions: CO( g ), CH ₄ ( g ), or C ₂ H ₂ ( g ).

The enthalpy of combustion of hard coal averages −35 kJ/g, that of gasoline, 1.28 $\times$ 10 ⁵ kJ/gal. How many kilograms of hard coal provide the same amount of heat as is available from 1.0 gallon of gasoline? Assume that the density of gasoline is 0.692 g/mL (the same as the density of isooctane).

Ethanol, C ₂ H ₅ OH, is used as a fuel for motor vehicles, particularly in Brazil.

(a) Write the balanced equation for the combustion of ethanol to CO ₂ ( g ) and H ₂ O( g ), and, using the data in Appendix G , calculate the enthalpy of combustion of 1 mole of ethanol.

(b) The density of ethanol is 0.7893 g/mL. Calculate the enthalpy of combustion of exactly 1 L of ethanol.

(c) Assuming that an automobile’s mileage is directly proportional to the heat of combustion of the fuel, calculate how much farther an automobile could be expected to travel on 1 L of gasoline than on 1 L of ethanol. Assume that gasoline has the heat of combustion and the density of n–octane, C ₈ H ₁₈ $(\text{Δ}{H}_{\text{f}}^{°}=\mathrm{-208.4}\text{kJ/mol;}$ density = 0.7025 g/mL).

Among the substances that react with oxygen and that have been considered as potential rocket fuels are diborane [B ₂ H ₆ , produces B ₂ O ₃ ( s ) and H ₂ O( g )], methane [CH ₄ , produces CO ₂ ( g ) and H ₂ O( g )], and hydrazine [N ₂ H ₄ , produces N ₂ ( g ) and H ₂ O( g )]. On the basis of the heat released by 1.00 g of each substance in its reaction with oxygen, which of these compounds offers the best possibility as a rocket fuel? The $\text{Δ}{H}_{\text{f}}^{°}$ of B ₂ H ₆ ( g ), CH ₄ ( g ), and N ₂ H ₄ ( l ) may be found in Appendix G .

How much heat is produced when 1.25 g of chromium metal reacts with oxygen gas under standard conditions?

Ethylene, C ₂ H ₂ , a byproduct from the fractional distillation of petroleum, is fourth among the 50 chemical compounds produced commercially in the largest quantities. About 80% of synthetic ethanol is manufactured from ethylene by its reaction with water in the presence of a suitable catalyst. ${\text{C}}_2{\text{H}}_4(g)+{\text{H}}_2\text{O}\left(g\right)⟶{\text{C}}_2{\text{H}}_5\text{OH}\left(l\right)$

Using the data in the table in Appendix G , calculate Δ H ° for the reaction.

The oxidation of the sugar glucose, C ₆ H ₁₂ O ₆ , is described by the following equation:
${\text{C}}_6{\text{H}}_{12}{\text{O}}_6(s)+6{\text{O}}_2(g)⟶6{\text{CO}}_2(g)+6{\text{H}}_2\text{O}\left(l\right)\text{Δ}\text{H}=\mathrm{-2816}\text{kJ}$

The metabolism of glucose gives the same products, although the glucose reacts with oxygen in a series of steps in the body.

(a) How much heat in kilojoules can be produced by the metabolism of 1.0 g of glucose?

(b) How many Calories can be produced by the metabolism of 1.0 g of glucose?

Propane, C ₃ H 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 O ₂ 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 O ₂ per liter.)

(c) The heat of combustion of propane is −2,219.2 kJ/mol. Calculate the heat of formation, $\text{Δ}{H}_{\text{f}}^{°}$ of propane given that $\text{Δ}{H}_{\text{f}}^{°}$ of H ₂ O( l ) = −285.8 kJ/mol and $\text{Δ}{H}_{\text{f}}^{°}$ of CO ₂ ( 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.

During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 kWh of heat provided by a natural gas furnace with 89% efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house).

(a) Assume that natural gas is pure methane and determine the volume of natural gas in cubic feet that was required to heat the house. The average temperature of the natural gas was 56 °F; at this temperature and a pressure of 1 atm, natural gas has a density of 0.681 g/L.

(b) How many gallons of LPG (liquefied petroleum gas) would be required to replace the natural gas used? Assume the LPG is liquid propane [C ₃ H ₈ : density, 0.5318 g/mL; enthalpy of combustion, 2219 kJ/mol for the formation of CO ₂ ( g ) and H ₂ O( l )] and the furnace used to burn the LPG has the same efficiency as the gas furnace.

(c) What mass of carbon dioxide is produced by combustion of the methane used to heat the house?

(d) What mass of water is produced by combustion of the methane used to heat the house?

(e) What volume of air is required to provide the oxygen for the combustion of the methane used to heat the house? Air contains 23% oxygen by mass. The average density of air during the month was 1.22 g/L.

(f) How many kilowatt–hours (1 kWh = 3.6 $\times$ 10 ⁶ J) of electricity would be required to provide the heat necessary to heat the house? Note electricity is 100% efficient in producing heat inside a house.

(g) Although electricity is 100% efficient in producing heat inside a house, production and distribution of electricity is not 100% efficient. The efficiency of production and distribution of electricity produced in a coal-fired power plant is about 40%. A certain type of coal provides 2.26 kWh per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation and distribution is 40%?