The Gas Laws 1. Boyle’s Law 2. Charles’ Law 3. Gay-Lussac’s Law 4. Avogadro’s Law
Boyle’s Law – at constant temperature, the volume of the gas increases as the pressure decreases. The volume of the gas decreases and the pressure increases. V↑ P↓ V o l u m e L P 1 V 1 = P 2 V 2 If you squeeze a gas sample, you make its volume smaller. Pressure (k. Pa)
Now. . . a container where the volume can change (syringe) Moveable piston ↕ Same temperature Volume is 100 m. L at 25°C Volume is 50 m. L at 25°C In which system is the pressure higher? (Which has the greater number of collisions with the walls and each other? )
Charles’ Law – at a constant pressure, the volume of a gas increases as the temperature of the gas increases and the volume decreases when the temperature decreases. • increase AKE • increase the speed of the particles • the walls of a flexible container expand – think of hot air balloons! V o l u m e V 1 V 2 = T 1 T 2 L Temperature (K)
A B Steel cylinder (2 L) contains 500 molecules of O 2 at 400 K Steel cylinder (2 L) contains 500 molecules of O 2 at 800 K 1. In which system do the O 2 molecules have the highest average kinetic energy? B 2. In which system will the particles collide with the container walls with the greatest force? B 3. In which system is the pressure higher? B
Gay-Lussac’s Law – the pressure of a gas is directly proportional to its absolute temperature at a constant volume. P 1 = P 2 T 1 T 2 Pressure (atm) Temperature (K)
To remember how these work. . . PTV Think “Public Tele Vision”
To remember which constants go with which law. . . Boyle’s Law – Temperature is constant BLT Charles’ Law – Pressure is constant Cheese Pizza Gay-Lussac’s Law – Volume is constant Green Veggies
Combined Gas Law P 1 V 1 = P 2 V 2 T 1 T 2 The equation is found on Table T. Note that all temperatures must be in Kelvin!
Units used to describe gas samples: Volume Liter (L) Milliliter (m. L) 1000 m. L = 1 L Temperature Kelvin ONLY Pressure Atmosphere (atm) Kilopascale (k. Pa) 1 atm = 101. 3 k. Pa 1 atm = 760 mm Hg 1 atm = 760 torr
Avogadro’s Law – equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. H 2 O 2 CO 2 1 mole of ANY gas takes up a volume of 22. 4 L at STP.
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Ideal Gases • Gases whose behavior can be predicted by the kinetic molecular theory are called ideal, or perfect, gases. No gases are truly ideal because no gas totally obeys all of the gas laws. • An ideal gas is an imaginary gas that is perfect and does follow everything perfectly.
Ideal Gases, continued An ideal gas does not condense to a liquid at low temperatures An ideal gas does not have forces of attraction or repulsion between particles An ideal gas is composed of particles that have no volume.
Real Gas Vs. Ideal Gas A real gas is most like an ideal gas when the real gas is at a low pressure and a high temperature. The gases that act most like ideal gases are the small mass ones – hydrogen and helium.
Diffusion • movement of particles from areas of high concentrations to areas of low concentration. • Gases diffuse and mix with other gases very rapidly due to their rapid motion. (Think ammonia, tuna or skunk smell. ) • It eventually reaches equilibrium and the mixture is homogeneous. Entropy is the randomness of particles. Effusion – the passage of gas under pressure through a small opening. (Gases effuse through a hole in your tire!)
Two More Laws!! Graham’s Law – Particles of low molar mass travel faster than heavier particles. Hydrogen effuses 4 times faster than oxygen. Dalton’s Law of Partial Pressure In a mixture of gases, each gas exerts a certain pressure as if it were alone. The pressure of each one of these gases is called the partial pressure. The total pressure of a mixture of gases is the sum of all of the partial pressures. Ptotal = PA + PB + PC
Example: A closed cylinder contains 3 L of He, 1 L of H 2 and the total pressure in the system is 800 torr. What is the partial pressure of the He? Ptotal = PA + PB + PC 3 L + 1 L = 4 L 4 L = 800 torr 4 4 → 1 L H 2 3 L He 4 L gas 200 torr 600 torr 800 torr AND 4 L = 800 torr 1 L = 200 torr
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