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Sec. 13.1: The Gas Laws Ch. 13: Gases

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Objectives State the relationships among pressure, temperature, and volume of a constant amount of gas. Apply the gas laws to problems involving the pressure, temperature and volume of a constant amount of gas.

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Review: The Kinetic Theory Ideally: Gas particles do not attract or repel each other. Gas particles are much smaller than the distances between them. That is, they have essentially NO volume compared to the space between them. Gas particles are in constant, random motion. No kinetic energy is lost when gas particles collide with each other or their container. All gases have the same average kinetic energy at a given temperature.

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In Reality …. Actual gases don’t obey all the assumptions made by the kinetic theory. Most gases DO approximate the behaviors assumed by the kinetic theory. (At extremely high pressures and low temperatures, gases do not behave ideally.) There are 3 factors that work together, when the amount of a gas is constant, to determine the behavior of a gas in the kinetic theory: temperature (T), volume (V), and pressure (P).

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What is the relationship between pressure and volume that is pictured here?

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Boyle’s Law If the number of particles and the temperature do not change, when the gas particles are pushed closer together, the number of collisions those particles have increases (less room, more collisions). Therefore, the pressure of the gas increases. If the volume is increased, the number of collisions will decrease and gas pressure will decrease. P & V are inversely proportional.

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Boyle’s Law: The volume of a given amount of gas held at a constant temperature varies inversely with the pressure. The plot of an inversely proportional relationship results in a downward curve.

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Boyle’s Law Mathematically, for two sets of conditions, P 1 V 1 = P 2 V 2 “1” represent the original conditions; “2” represent new conditions. If a gas occupies 2.0 L at 2.5 atm., what volume will it occupy at 4 atm.? P 1 = 2.5 atm P 2 = 4 atm V 1 = 2.0 L V 2 = ? Solve for V 2

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Boyle’s Law Problems A sample of helium gas in a balloon is compressed from 4.0 L to 2.5 L at a constant temperature. If the pressure of the gas in the 4.0 L volume is 210 kPa, what will the pressure be at 2.5 L? A sample of neon gas occupies L at atm. What will its volume be at 29.2 kPa of pressure?

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Charles’s Law As the temperature of a gas increases, so does its volume when the amount of gas and pressure do not change. How does the KMT explain this?

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Charles’s Law Charles’s law states that the volume of a given mass of gas is directly proportional to its Kelvin temperature at constant pressure. Mathematically, To convert 0 C into K, use the expression: K = C

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The Kelvin Scale The Kelvin scale is based on a concept called absolute zero. Absolute zero is, theoretically, the lowest possible temperature that can be reached. At absolute zero (K = 0 and C = ), it is theorized that the motion of all particles of matter ceases. The particles have no movement and, so, the particles have no energy.

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Charles’s Law The graph of a directly proportional relationship is an upward sloping straight line.

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Charles’s Law Problems A gas sample at 40 0 C occupies a volume of 2.32 L. If the temperature is raised to 75 0 C, what will the volume be, assuming the pressure remains constant? A gas at 89 0 C occupies a volume of 0.67 L. At what Celsius temperature will the volume be increased to 1.12 L? What is the volume of air in a balloon that occupies L at 25 0 C if the temperature is lowered to 0 0 C?

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Recall... Gas pressure results from the collisions of gas particles with the walls of their container. If the temperature is increased, the particles will move faster. This will increase the number of collisions (and their force). So an increase in temperature will result in an increase of gas pressure.

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Gay-Lussac’s Law Gay-Lussac’s law states that the pressure of a given mass of gas varies directly with the Kelvin temperature when the volume remains constant.

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Gay-Lussac’s Law Mathematically,

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Gay-Lussac’s Law Problems The pressure of a gas in a tank is 3.20 atm at 22 0 C. If the temperature rises to 60 0 C, what will be the gas pressure in the tank? A gas in a sealed container has a pressure of 125 kPa at a temperature of 30 0 C. If the pressure in the container is increased to 201 kPa, what is the new temperature? Helium gas in a 2 L cylinder is under 1.12 atm of pressure. At C, that same gas sample has a pressure of 2.56 atm. What was the initial temperature of the gas in the cylinder?

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The Combined Gas Law Boyle’s, Charles’s and Gay-Lussac’s Laws can be combined into a single law. The combined gas law states that the relationship among pressure, volume and temperature of a fixed amount of gas.

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The Combined Gas Law Relationships between the variables do not change. For example, P and V are still inversely proportional. The equation for the combined gas law is: P 1 V 1 = P 2 V 2 T 1 T 2

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The Combined Gas Law Problems A gas at 110 kPa and 30 0 C fills a flexible container with an initial volume of 2.0 L. If the temperature is raised to 80 0 C and the pressure is increased to 440 kPa, what is the new volume? At STP, a gas sample occupies 30 mL. If the temperature is increased to 30 0 C and the entire sample is transferred to a 20 mL container, what will be the gas pressure inside the container?

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