Gas Laws PDF

GASES GENCHEM LEARNING OBJECTIVES I will be able to calculate the pressure or volume of a gas at different conditions I will be able to determine the pressure of a gas mixture or of its components I will be able to determine the amount of products or reactants involved in a gas...

GASES GENCHEM LEARNING OBJECTIVES I will be able to calculate the pressure or volume of a gas at different conditions I will be able to determine the pressure of a gas mixture or of its components I will be able to determine the amount of products or reactants involved in a gas phase reaction I will be able to discuss the properties and behavior of gases in terms of its molecular composition  GASES ARE ABUNDANT IN OUR SURROUNDINGS, SUCH AS IN THE ENVIRONMENT, AT HOME AND IN OTHER PLACES. In the air, which supplies us with the gases we breathe In the kitchen, wherein a gas (liquid petroleum gas) is used for heating or cooking In the hospital, wherein gases are used to aid the breathing of patients  In the automobile, wherein gases are burned in order to make the cars In carbonated drinks, wherein a gas (carbon dioxide) makes the drinks refreshing  THE KINETIC MOLECULAR THEORY 1. Molecules of gases are relatively apart, and don’t attract each other. 2. Molecules of gases are in constant rapid, chaotic motion, colliding with each other and the walls of the container in random fashion, generating gas pressure. 3. All molecular collision are perfectly elastic, resulting in no decrease in total kinetic energy. 4. The average kinetic energy of gas molecules is proportional to the absolute temperature. At the same absolute temperature, the average kinetic energies of the molecules of all gases are the same.  PRESSURE the amount P = F/A of force exerted per P - Pressure F - Force unit A - Area VARIOUS UNITS FOR PRESSURE pounds per square inch (psi) kilopascal (KPa) newton per square meter, N/m2 atmosphere (atm) Torr (or mmHg) OTHER PARAMETERS VOLUME ⚬ L ⚬ mL TEMPERATURE ⚬ Celsius ⚬ Fahrenheit ⚬ Kelvin GAS LAWS Boyle’s Law Charles’ Law Avogadro’s Law BOYLE’S LAW The volume of a given amount of gas is inversely proportional to its pressure at constant temperature valid only if the amount of the gas and the temperature is constant. P1V1 = P2V2 BOYLE’S LAW As volume increases, the pressure of a gas decreases proportionally, and vice versa. Temperature is constant A gas sample occupies a volume of 2.5 L at a pressure of 1.5 atm. What would be the volume of the gas if its pressure is reduced to 1 atm at the same temperature? Given: Formula: Solve: P1 = 1.5 atm P1V1 = P2V2 P2 = 1 atm (1.5 atm)(2.5L) V2 = V1 = 2.5L P1V1 1 atm V2 = ? V2 = P2 V2 = 3.75 L  The gas inside a balloon has a volume of 15.0 L at a pressure of 2.0 atm. Calculate the pressure of the gas if its volume is compressed to 10.0 L at the same temperature. Given: Formula: Solve: P1 = 2.0 atm P1V1 = P2V2 P2 = ? (2.0 atm)(15.0L) P2 = V1 = 15.0 L P1V1 10.0 L V2 = 10.0 L P2 = V2 P2 = 3 atm  A gas occupies 12.3 liters at a pressure of 40.0 mm Hg. What is the volume when the pressure is increased to 60.0 mm Hg? Given: Formula: Solve: P1 = 40 mmHg P1V1 = P2V2 P2 = 60.0 mmHg (40mmH𝑔)(12.3𝐿) V2 = V1 = 12.3 L P1V1 60 mmHg V2 =? V2 = P2 V2 = 8.2 L  A gas exerts a pressure of 3.0kPa when it occupies a 12.0L vessel at 20ºC.what pressure would the gas exert at 20ºC if same gas example is transferred to a 9.0L vessel. Given: Formula: Solve: P1 = 3.0 kPa P1V1 = P2V2 P2 = ? (3.0 𝑘𝑃𝑎)(12 𝐿) P2 = V1 = 12.0 L P1V1 9.0 L V2 = 9.0 L P2 = V2 P2 = 4 kPa CHARLES’S LAW The volume of a given amount of gas is directly proportional to its absolute temperature at constant pressure valid only if the amount of the gas and the pressure is constant. the temperature should be expressed in the unit Kelvin (K). CHARLES’S LAW A gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. At 30 oC, the volume of a sample of air was 5.8 L. What would be the volume of the air sample if it is heated to 60 C at the same pressure? o Given: Formula: Solve: V1 = 5.8 L V1 V2 V2 = ? = (333 𝐾)(5.8 𝐿) T1 T2 T1 = 30 oC (303 K) V2 = 303 K T2V 1 T2 = 60 oC (333 K) V2 = T1 V2 = 6.37 L Take note that the temperature must be in KELVIN Celsius to Kelvin - Celsius + 273  A given amount of oxygen gas has a volume of 25.0 L at a temperature of 37 oC and a pressure of 1.0 atm. At what temperature would this gas occupy a volume of 22.0 L at a pressure of 1.0 atm? Given: Formula: Solve: V1 = 25.0 L V1 V2 V2 = 22.0 L = (310)(22) T1 T2 T1 = 37 oC (310 K) T2 = 25 T1 V 2 T2 = ? T2 = V1 T2 = 273 K  4.40 L of a gas is collected at 50.0°C. What will be its volume upon cooling to 25.0°C? Given: Formula: Solve: V1 = 4.40 L V1 V2 V2 = ? = (298)(4.40) T1 T2 T1 = 50 oC (323 K) V2 = 323 T2 V 1 T2 = 25 oC (298 K) V2 = T1 V2 = 4 L AVOGADRO’S LAW At constant temperature and pressure, two gases with of the same volume will contain the same number of molecules  PRACTICE EXERCISE 1. A 6.0 L sample at 25°C and 2.00 atm of pressure contains 0.5 mole of a gas. If an additional 0.25 mole of gas at the same pressure and temperature are added, what is the final total volume of the gas? 2. 11.2 L sample of gas is determined to contain 0.5 moles of nitrogen. At the same temperature and pressure, how many moles of gas would there be in a 20 L sample? GAY-LUSSAC’S LAW A gas's pressure is directly proportional to temperature. We assume a constant volume and a constant number of moles. This equation can be rearranged into an equation known as the combined gas law, which holds true for a given amount of COMBINED GAS LAW The combined gas law reduces to Boyle’s Law, if temperature is kept constant (i.e. T1 = T2) It also reduces to Charles’s Law, if pressure is kept constant (i.e. P1 = P2): It will also show that pressure of a gas is directly proportional to its absolute temperature, if the volume is kept constant (i.e. V1 = V2):  IDEAL GAS EQUATION The ideal gas law states that for a specific amount of gas, the product of pressure and volume is directly proportional to the absolute temperature. The ideal gas law states that all gases contain the same number of gas molecules when under equal temperature, volume, and pressure.  IDEAL GAS EQUATION The ideal gas law states that all gases contain the same number of gas molecules when under equal temperature, volume, and pressure. Gas constant: 0.0821 DALTON’S LAW OF PARTIAL PRESSURE Dalton’s law of partial pressures is a gas law which states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas in the mixture. DALTON’S LAW OF PARTIAL PRESSURE