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Gas Laws Chemistry 9(A) Gas Laws Learning Objectives • Describe the relationships between volume, pressure, number of moles, and temperature for an ideal gas • Perform calculations that predict values for variables using – – – – – Boyle’s law Charles’ law Avogadro’s law Ideal gas law Dalton’s law of partial pressure Variables Affecting Gases • Gases can be characterized by their – – – – Volume ( V ) Temperature ( T ) Number of moles ( n ) Pressure ( P ) Gas Relationships • Gas law – law which describes the relationship between two or more variables of a gas • Variables may be directly or inversely related – Direct relationship – values of variables increase or decrease together – Inverse relationship – as the value one variable goes up, the value of the other variable goes down • Variables not included in the gas law remain constant Charles’ Law • Charles’ law describes the relationship between temperature and volume, when the pressure and amount of gas are constant • Volume and temperature are directly proportional on the Kelvin scale Charles’ Law • Temperature is directly proportional to kinetic energy – Kinetic energy – energy of motion – At higher temperatures, gas particles • Have more kinetic energy • Move more • Spread out Ex) Volume of a gas when T1 < T2 Temperature Scales Celsius vs. Kelvin scale • Must use kelvin in Charles’ law calculations • Celsius to Kelvin scale Ex) 25 ∘C + 273 = 298 K Charles’ Law Calculation Ex) A 2.4 L volume of gas is heated from 298 K to 405 K. What new volume does it occupy? 1. 2. Write unknown and givens 3. 4. Convert units and find intermediates, if needed Plug in and solve 5. Make sure the answer is reasonable Identify the formula and rearrange, if needed Boyle’s Law • Boyle’s law describes relationship between pressure and volume when the temperature and amount of gas remain constant • Pressure and volume are inversely proportional Pressure Units Units of pressure • Atmospheres (atm) • Millimeters of mercury (mmHg) • Kilopascals (kPa) Equivalent amounts • 1 atm = 760 mmHg = 101.3 kPa Ex) How many kilopascals are equal to 5.00 atm? Boyle’s Law Calculation Ex) The initial pressure of a 3.0 L sample of gas was 2.5 atm. At what pressure will the volume of the gas expand to 5.0 L? 1. 2. Write unknown and givens Identify the formula and rearrange, if needed 3. 4. Convert units and find intermediates, if needed Plug in and solve 5. Make sure the answer is reasonable Avogadro's Law • Avogadro’s law describes the relationship between number of moles and volume, when temperature and pressure remain constant • Number of moles of gas are directly proportional to volume Avogadro’s Law Calculation Ex) How many moles of carbon monoxide gas are present in a 9.6 L sample if 4.2 moles were contained in 5.0 L sample? 1. 2. Write unknown and givens Identify the formula and rearrange, if needed 3. 4. Convert units and find intermediates, if needed Plug in and solve 5. Make sure the answer is reasonable Ideal Gas Law • Combining Charles’, Boyle’s, and Avogadro’s laws gives the following equation: • A gas always has the same relationships between its variables – Charles –– volume and temperature are directly proportional – Boyle –– pressure and volume are indirectly proportional – Avogadro –– number of moles and volume are directly proportional • R is the ideal gas constant Ideal Gas Law • Ideal gas law describes the relationship between all four variables: temperature, volume, number of moles, and pressure – Potential values for R depending on the pressure unit used • 0.0821 L ·atm = 8.31 L · kPa = 62.4 L · mmHg mol ·K mol ·K mol ·K Ideal Gas Law Calculation Ex) What is the volume of a 1.42 mol sample of O2 gas at 25 °C and 1.25 atm of pressure? 1. Write unknown and givens 3. Convert units and find intermediates, if needed 25 °C + 273 = 298 K 4. Plug in and solve 1. Identify the formula and rearrange, if needed 5. Make sure the answer is reasonable Dalton’s Law of Partial Pressure • Dalton’s law of partial pressure describes the relationships in a mixture of gases • Total pressure of a gas mixture is equal to the sum of the partial pressures of the individual gases Dalton’s Law Calculation Ex) A mixture of gases containing methane, CH4, ethane, C2H6, and propane, C3H8, gases has a total pressure of 975 mmHg. If the partial pressures of CH4 and C2H6 are 235 mmHg and 450mmHg, respectively, what is the partial pressure of C3H8 ? 1. 2. Write unknown and givens Identify the formula and rearrange, if needed 3. 4. Convert units and find intermediates, if needed Plug in and solve 5. Make sure the answer is reasonable Gas Laws Learning Objectives • Describe the relationships between volume, pressure, number of moles, and temperature for an ideal gas • Perform calculations that predict values for variables using – – – – – Boyle’s law Charles’ law Avogadro’s law Ideal gas law Dalton’s law of partial pressure