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- In the 1880s, Frederick Trouton noted that the enthalpy of vaporization of 1 mol pure liquid is approximately 88 times the boiling point, Tb, of the liquid on the Kelvin scale. This relationship is called Troutons rule and is represented by the thermochemical equation liquid gas H = 88 Tb, joules Combined with an empirical formula from chemical analysis, Troutons rule can be used to find the molecular formula of a compound, as illustrated here. A compound that contains only carbon and hydrogen is 85.6% C and 14.4% H. Its enthalpy of vaporization is 389 J/g, and it boils at a temperature of 322 K. (a) What is the empirical formula of this compound? (b) Use Troutons rule to calculate the approximate enthalpy or vaporization or one mole of the compound. Combine the enthalpy of vaporization per mole with that same quantity per gram to obtain an approximate molar mass of the compound. (c) Use the results of parts (a) and (b) to find the molecular formula of this compound. Remember that the molecular mass must be exactly a whole-number multiple of the empirical formula mass, so considerable rounding may be needed.You have the six pieces of metal listed below, plus a beaker of water containing 3.00 102 g of water. The water temperature is 21.00 C. (a) In your first experiment you select one piece of metal and heat it to 100 C, and then select a second piece of metal and cool it to 10 C. Both pieces of metal are then placed in the beaker of water and the temperatures equilibrated. You want to select two pieces of metal to use, such that the final temperature of the water is as high as possible. What piece of metal will you heat? What piece of metal will you cool? What is the final temperature of the water? (b) The second experiment is done in the same way as the first. However, your goal now is to cause the temperature to change the least, that is, the final temperature should be as near to 21.00 C as possible. What piece of metal will you heat? What piece of metal will you cool? What is the final temperature of the water?Ethyl alcohol, C2H5OH, is the intoxicating agent in liquor. Burning 1.00 g of ethyl alcohol in an excess of oxygen at 23.28C and constant volume releases 29.52 kJ of heat. When 7.40 g of ethyl alcohol is burned in oxygen under the same conditions in a bomb calorimeter, the temperature of the bomb and water rises from 23.28C to 48.04C. The bomb holds 0.750 kg of water. (a) What is q for the combustion of the ethyl alcohol in the bomb calorimeter? (b) What is qH2O? (c) What is qcal? (d) What is the heat capacity of the calorimeter?
- 9.86 You make some iced tea by dropping 134 g of ice into 500.0 mL of warm tea in an insulated pitcher. If the tea is initially at 20.0°C and the ice cubes are initially at 0.0°C, how many grams of ice will still be present when the contents of the pitcher reach a final temperature? The tea is mostly water, so assume that it has the same density (1.0 g/mL), molar mass, heat capacity (75.3 J K-1 mol-1), and heat of fusion (6.0 kJ/mol) as pure water. The heat capacity of ice is 37.7 J K-l mol-l.As a system increases in volume, it absorbs 52.5 J of energy in the form of heat from the surroundings. The piston is working against a pressure of 0.500 atm. The final volume of the system is 58.0 L. What was the initial volume of the system if the internal energy of the system decreased by 102.5 J?9.102 A runner generates 418 kJ of energy per kilometer from the cellular oxidation of food. The runner's body must dissipate this heat or the body will overheat. Suppose that sweat evaporation is the only important cooling mechanism. If you estimate the enthalpy of evaporation of water as 44 kJ/mol and assume that sweat can he treated as water, describe how you would estimate the volume of sweat that would have to be evaporated if the runner runs a 10-km race.
- Isooctane is a primary component of gasoline and gives gasoline its octane rating. Burning 1.00 mL of isooctane (d=0.688g/mL) releases 33.0 kJ of heat. When 10.00 mL of isooctane are burned in a bomb calorimeter, the temperature in the bomb and water rises from 23.2C to 66.5C. The bomb contains 1.00 kg of water. What is the heat capacity of the calorimeter?Which is the least expensive source of energy in kilojoules per dollar: a box of breakfast cereal that weighs 32 ounces and costs $4.23, or a liter of isooctane (density, 0.69 19 g/mL) that costs $0.45? Compare the nutritional value of the cereal with the heat produced by combustion of the isooctane under standard conditions. A 1.0-ounce serving of the cereal provides 130 Calories.9.104 An engineer is using sodium metal as a cooling agent in a design because it has useful thermal properties. Looting up the heat capacity, the engineer finds a value of 28.2 J mol-l °C-l. Carelessly, he wrote this number down without units. As a result, it was later taken as specific heat. (a) What would he the difference between these two values? (b) Would the engineer overestimate the ability of sodium to remove heat from the system or underestimate it because of this error? Be sure to explain your reasoning.
- In earlier times, ethyl ether was commonly used as an anesthetic. It is, however, highly flammable. When five milliliters of ethyl ether, C4H10O(l)(d=0.714g/mL), are burned in a bomb calorimeter, the temperature rises from 23.5C to 39.7C. The calorimeter contains 1.200 kg of water and has a heat capacity of 5.32 kJ/C. (a) What is qH2o? (b) What is qcal? (c) What is q for the combustion of 5.00 mL of ethyl ether? (d) What is q for the combustion of one mole of ethyl ether?A bomb calorimetric experiment was run to determine the enthalpy of combustion of ethanol. The reaction is C2H5OH() + 3 O2(g) 2 CO2(g) + 3 H2O() The bomb had a heat capacity of 550 J/K, and the calorimeter contained 650 g of water. Burning 4.20 g of ethanol, C2HsOH() resulted in a rise in temperature from 18.5 C to 22.3 C. Calculate U for the combustion of ethanol, in kJ/mosl.9.91 You want to heat the air in your house with natural gas (CH4). Assume your house has 275 m2(ahout 2800 ft2) of floor area and that the ceilings are 2.50 m from the floors. The air in the house has a molar heat capacity of 29.1 J mol-l K-l. (The number of moles of air in the house may he found by assuming that the average molar mass of air is 28.9 g/mol and that the density of air at these temperatures is 1.22 g/L.) What mass of methane do you have to burn to heat the air from 15.0 to 22.0°C?