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Sketch the situation Indicate the conditions in the container of argon before and after the change in temperature and pressure List the known and unknown variables Known:
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V1 200 L P1 1013 kPa T1 273 K P2 145 kPa T2 120 K R 831 Pa m3/mol K Margon 399 g/mol
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T1 P1 V1 273 K 1013 kPa 200 L T2 P2 V2 120 K 145 kPa
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Unknown:
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V2 moles of argon mass of argon sample
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a Use the combined gas law and solve for V2
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P1V1 T1 P2V2 T2 P1V1T2 P2T1 (1013 kPa)(200 L)(120 K) (145 kPa)(273 K)
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Substitute P1 1013 kPa, P2 145 kPa, V1 200 L, T1 273 K, T2 120 K
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Math Handbook
Isolating a Variable page 845
61 L b Use the ideal gas law and solve for n PV nRT n
PV RT (1013 103 Pa)(00200 m3) (831 Pa m3/mol K)(273 K)
Substitute P 1013 103 Pa, V R 831 m3/mol K, T 273 K
00200 m3,
0893 mol c Use the molar mass to convert from moles of argon in the sample to mass of the sample m Mn Substitute M 399 g/mol, n 0893 mol margon sample (399 g/mol)(0893 mol) 356 g
Evaluate the Answer
Are the units correct The volume, V2, is in liters, and the mass of the sample is in grams Is the magnitude realistic The change in volume is consistent with an increase in pressure and decrease in temperature The calculated mass of the argon sample is reasonable
13 States of Matter
6 A tank of helium gas used to inflate toy balloons is at a pressure of 155 106 Pa and a temperature of 293 K The tank s volume is 0020 m3 How large a balloon would it fill at 100 atmosphere and 323 K 7 What is the mass of the helium gas in the previous problem The molar mass of helium gas is 400 g/mol 8 A tank containing 2000 L of hydrogen gas at 00 C is kept at 156 kPa The temperature is raised to 95 C, and the volume is decreased to 175 L What is the new pressure of the gas 9 The average molar mass of the components of air (mainly diatomic oxygen gas and diatomic nitrogen gas) is about 29 g/mol What is the volume of 10 kg of air at atmospheric pressure and 200 C
Thermal Expansion
As you applied the combined gas law, you discovered how gases expand as their temperatures increase When heated, all forms of matter solids, liquids, and gases generally become less dense and expand to fill more space This property, known as thermal expansion, has many useful applications, such as circulating air in a room When the air near the floor of a room is warmed, gravity pulls the denser, colder air near the ceiling down, which pushes the warmer air upward This circulation of air within a room is called a convection current Figure 13-5 shows convection currents starting as the hot air above the flames rises You also can see convection currents in a pot of hot, but not boiling, water on a stove When the pot is heated from the bottom, the colder and denser water sinks to the bottom where it is warmed and then pushed up by the continuous flow of cooler water from the top This thermal expansion occurs in most liquids A good model for all liquids does not exist, but it is useful to think of a liquid as a finely ground solid Groups of two, three, or more particles move together as if they were tiny pieces of a solid When a liquid is heated, particle motion causes these groups to expand in the same way that particles in a solid are pushed apart The spaces between groups increase As a result, the whole liquid expands With an equal change in temperature, liquids expand considerably more than solids, but not as much as gases Why ice floats Because matter expands as it is heated, you might predict that ice would be more dense than water, and therefore, it should sink However, when water is heated from 0 C to 4 C, instead of expanding, it contracts as the forces between particles increase and the ice crystals collapse These forces between water molecules are strong, and the crystals that make up ice have a very open structure Even when ice melts, tiny crystals remain These remaining crystals are melting, and the volume of the water decreases until the temperature reaches 4 C However, once the temperature of water moves above 4 C, its volume increases because of greater molecular motion The practical result is that water is most dense at 4 C and ice floats This fact is very important to our lives and environment If ice sank, lakes would freeze from the bottom each winter and many would never melt completely in the summer
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