the behavior of gases chapter 5. kinetic theory review the following five tenets are the basis for...
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The Behavior of GasesChapter 5
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Kinetic Theory Review
• The following five tenets are the basis for ideal gases
• Gases consist of hard spherical particles
• Particles have insignificant volume
• There are large distances between particles
• There are NO attractive or repulsive forces between particles
• Particles are in constant, random motion with elastic collisions
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Variables and Equations
• 4 variables are pressure (P) in kilopascals, temperature (T) in kelvins, volume (V) in liters, and number of moles (n).
• Help to understand everyday applications such as airbags, scuba-diving equipment, and hot-air balloons.
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Compressibility
• Why are gases compressed more easily than liquids or solids?
• How does the overall volume of the particles in a gas compare to the overall volume of the gas
• How does an airbag work?
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Amount of a Gas
• What happens to the pressure if you double the amount of particles in a rigid container?
• How does an aerosol can work?
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Volume
• If you double the volume of a rigid container, what can be said about the pressure?
• What about if you halve the volume?
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Temperature
• When you increase the temperature of gas molecules in a container, what happens to the pressure?
• The molecules gain more KE, move faster, and thus create more pressure.
• If you leave a bag of potato chips in the sun, it will bulge at the seams
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Gas Laws
• Boyle’s Law
• Charles’ Law
• Gay-Lussac’s Law
• Combined Gas Law
• Ideal Gas Law
• Dalton’s Law
• Graham’s Law
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Boyle’s Law
• As volume increases, pressure _________.
• Therefore, volume and pressure are inversely related
• We can show this by P1V1 = P2V2
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Charles’ Law
• As temperature increases, volume _________.
• Therefore temperature and volume are directly related.
• We can show this by
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Gay-Lussac’s Law
• As the pressure of an enclosed gas increases, the temperature __________.
• Therefore temperature and pressure are directly related.
• We can show this by
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The Combined Gas Law
• We can combine the previous three laws into one law that involves P, T and V.
• The combined gas law is written as
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The Ideal Gas Law
• To calculate the number of moles of a contained gas, we use the variable ‘n’
• The ideal gas law is PV = nRT
• R is known as the ideal gas constant
• R = 8.31 (if pressure is in kPa)
R = 0.0821 (if pressure is in atm)
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Ideal Gas Law
• PV = nRT
• What are the units on R?
• Can we derive the value for R?
• Remember that at STP, T = 273 K, P = 101.3 kPa, n = 1 mol, V = 22.4 L
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Ideal vs. Real
• Real gases differ most from an ideal gas at low temperatures and high pressures
• Remember, in reality, there are attractive forces between molecules
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Dalton’s Law
• Also known as the law of partial pressures: In a mixture of gases, the total pressure is the sum of the partial pressures of the gases
• Simply, Ptotal = P1 + P2 + P3 + …
• Why would a climber at the top of Mt. Everest care about Dalton’s Law?
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Graham’s Law
• Gases with a lower molar mass will diffuse faster than gases with a larger mass
• It makes sense that a lighter object will have to move faster to have the same energy as a larger object moving slowly
• We can show this law as
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How to Solve Problems
Here is a sample problem:
5 moles of gas is heated to 400K in a 2.5 L container. What is the pressure of the gas?
• Identify and write down variables.
n = 5, T = 400K, V = 3.5 L
N – 5, T = 5, 400