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## Gas Laws

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**Gas Pressure**• Pressure is defined as force per unit area • Gas pressure is defined as collisions with the walls of a container • Internal collisions between molecules don't count • As molecules move faster more collisions, hence greater pressure • Measured using a barometer • Pressure can also be changed by changing the area struck by the particles**When Dalton studied the properties of gases, he found that**each gas in a mixture exerts pressure independently of the other gases present**Dalton’s Law of Partial Pressures**• States that the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases in the mixture**Dalton’s Law of Partial Pressures**• the pressure contributed by a single gas is called its partial pressure • Partial pressure depends on the # of moles of gas, size of the container, and temperature of the mixture • At a given temperature and pressure, the partial pressure of 1 mole of any gas is the same**Dalton’s Law of Partial Pressures**Ptotal = P1 + P2 + P3 + …Pn • Ptotal represents the total pressure of the mixture of gases, P1, P2, P3…represents the partial pressures**Example**• What is the partial pressure of hydrogen gas in a mixture of hydrogen and helium if the total pressure is 600 mmHg and the partial pressure of helium is 439 mmHg? Ptotal = P1 + P2 + P3 + …Pn 600 mmHg = 439 mmHg + PHydrogen PHydrogen = 161 mmHg**Practice 1**Find the total pressure for a mixture that contains four gases with partial pressures of 5.00 kPa, 4.56 kPa, 3.02 kPa, and 1.20 kPa. 13.78 kPa**Practice 2**Find the partial pressure of carbon dioxide in a gas mixture with a total pressure of 30.4 kPa if the partial pressures of the other two gases in the mixture are 16.5 kPa, and 3.7 kPa. 10.2 kPa**Robert Boyle**• Performed experiments to study the relationship between pressure and the volume of a gas • Displayed that under constant temperature, doubling of the pressure would result in the volume being cut in half and vice versa • Discovered that pressure and volume are inversely proportional**Boyle’s Law**• States that volume of a given amount of gas held at constant temperature varies inversely with the pressure P1V1 = P2V2 • P1 & V1 represent the initial set of conditions for the gas and P2 & V2 represent the new set of conditions for the gas**Boyle’s Law**• If you know any 3 of the 4 values for a gas at constant temperature, you can solve for the 4th by rearranging the equation • Example P2 = P1V1 V2 which can be done for any of the values in the equation**Example**The volume of a gas at 99.0 kPa is 300.0 mL. If the pressure is increased to 188 kPa, what will be the new volume? P1V1 = P2V2 V2 = P1V1 = (99 kPa)(300 mL) P2 188 kPa 158 mL**Practice 1**• The pressure of a sample of helium in a 1.00-L container is 0.988 atm. What is the new pressure if the sample is placed in a 2.00-L container? 0.494 atm**Practice 2**• Air trapped in a cylinder fitted with a piston occupies 145.7 mL at 1.08 atm pressure. What is the new volume of air when the pressure is increased to 1.43 atm by applying force to the piston? 110mL or 0.110 L**Homework**Dalton’s Law of Partial Pressures and Boyle’s Law Handout**Problem 10**An ion with 8 protons, 8 neutrons, and 10 electrons is represented by • Ne • O+2 • O-2 • O**Problem 11**• What is the mass number of an atom which contains 28 protons, 28 electrons, and 34 neutrons? • 28 • 56 • 62 • 90**The chart shows isotopes of some common elements. In what**two properties do the isotopes of carbon differ? Atomic number and number of neutrons Atomic mass and number of neutrons Atomic mass and number of protons Number of protons and number of neutrons Problem 12**Jacques Charles**• French physicist that studied the relationship between volume and temperature • Observed that volume rose as temperature did when the pressure was held constant**Charles’s Law and KMT**• As stated in the KMT, at higher temperatures, gas particles move faster, striking each other and the walls of their container more frequently and with greater force • If pressure is constant, volume must increase so the particles have farther to travel before striking the walls, which decrease the frequency at which the particles strike the walls of the container**Charles’s Law**• States that the volume of a given mass of gas is directly proportional to its Kelvin temperature at constant pressure V1 = V2 T1 T2 • V1 and T1 represent initial conditions and V2 and T2 represent the final conditions of the gas • TEMPERATURE MUST BE IN KELVINS IN ORDER TO USE CHARLES’S LAW TK = 273 + TC TK is the temperature in Kelvin and TC is the Celsius temperature**Isolating a Variable**Charles’s Law V1 = V2 T1 T2 • Cross Multiply V1T2 = V2T1 • Isolate the variable by dividing on both sides V1T2 = V2T1 T2 T2 V1 = V2T1 T2**Example**A gas at 89˚C occupies a volume of 0.67L. At what Celsius temperature will the volume increase to 1.12L? TK= 273 + 89 = 362K V1 = V2 T1 T2 T2 = T1V2 V1 T2 = (362 )(1.12) = 605 K .67 TC = 605 – 273 = 332 ˚C**Practice 1**The Celsius temperature of a 3.00-L sample of gas is lowered from 80˚C to 30˚C. What will be the resulting volume of this gas? 2.58L**Practice 2**What is the volume of the air in a balloon that occupies 0.620L at 25˚C if the temperature is lowered to 0˚C? 0.56L**Joseph Gay-Lussac**• Studied the relationship between temperature and pressure of a contained gas at a fixed volume • Discovered that temperature in Kelvin and pressure are directly proportional**Gay-Lussac’s Law**• States that the pressure of a given gas varies directly with the Kelvin temperature when the volume remains constant P1= P2 T1 T2 • P1 and T1 are the initial conditions and P2 and T2 are the final conditions of the gas**Example**A gas in a sealed container has a pressure of 125kPa at a temperature of 30°C. If the pressure in the container is increased to 201 kPa, what is the new temperature? TK = 273 + 30 = 303K P1= P2 T1 T2 T2 = T1P2 P1 T2 = (303)(201) = 487K 125 T2= 487-273 = 214°C**Practice 1**The pressure in an automobile tire is 1.88atm at 25°C. What will be the pressure if the temperature warms up to 37°C? 1.96atm**Practice 2**If a gas sample has a pressure of 30.7 kPa at 0°C, what would the temperature have to be to lower the pressure to 28.4 kPa? -21°C**Homework**• Charles’s Law • Gay-Lussac’s Law**Problem 13**What is the chemical formula for a compound formed from calcium ions (Ca2+) and chloride ions (Cl–1)? • a. CaCl • b. Ca2Cl • c. CaCl2 • d. Ca2Cl2**Problem 14**What is the correct formula for aluminum oxide? • A AlO • B Al3O2 • C AlO2 • D Al2O3**Combined Gas Law**• Combination of Boyle’s, Charles’s, & Gay-Lussac’s Laws • States the relationship among pressure, volume and temperature of a fixed amount of gas • Pressure is inversely proportional to volume • Pressure is directly proportional to temperature and temperature is directly proportional to volume**Combined Gas Law**P1V1 = P2V2 T1 T2