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## Gases

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**Gases**• Mr. Solsman • Chapter 13**Gases**• The Nature of Gases • The Molecular Basis of Gas Behavior • Pressure • Compressibility • Diffusion**The Nature of Gases**• Gases expand to fill their container. • Gases exert pressure on their container. • Gases are compressible.**The Molecular Basis of Gas Behavior**• Gas molecules are in constant motion. • Gas molecules are small compared to the distances between them. • Collisions between molecules are elastic. • The collisions of gas molecules with other objects creates pressure.**Units of Pressure**• 760 mmHg (aka 760 Torr) • = 1.000 atm • = 101.3 kPa • = 14.69 psi**Gas Laws**• Avogadro’s Hypothesis • Boyle’s Law • Charles’ Law • Gay-Lussac’s Law • The Combined Gas Law • Ideal Gas Law • Dalton’s Law • Graham’s Law**AVOGADRO’S HYPOTHESIS**- Equal volumes of gases at the same temperature and pressure have an equal number of molecules.**BOYLE’S LAW**Pressure is inversely proportional to the volume if the temperature and quantity are constant. Temperature, T, is measured in Kelvin and quantity, n, in moles. PV = k1if T and n are constant P1V1 = P2V2**PROBLEM SET**1. What is the pressure of a gas if 4.50 liters at 2.5atm of pressure is changed to a volume of 5.00 liters? 2.The volume of a gas is 22. 9 ml at 345mm of Hg. What is the volume at 500. mm of Hg?**CHARLES’ LAW**Observation made by Charles: For 1 liter of any gas at 00C and 1 atm, a change in temperature of 10C changes the volume by 1/273 of the original volume. The volume of a gas is directly proportional to the Kelvin temperature if quantity and pressure are constant. V / T = k2if n and P V1 /V2 = T1 /T2are constant**PROBLEM SET**1.The volume of a gas is 44.3ml at 250C. What is the volume at 100.0C? 2.The volume of a gas is 19.4 liters at -450C. What is the volume at standard state temperature? 3.If the volume of a gas is 56.4m3 at 750C, what temperature in 0C changes the volume to 40.0m3?**GAY-LUSSAC’S LAW**The pressure exerted by a gas is directly proportional to the Kelvin temperature if volume and quantity are held constant. P/T = k3 P1 / T1 = P2 / T2 What are the implications of 0 K on molecular motion and Kelvin temperature on KE?**1. The volume of a gas is 34.6 cm3 at 170C and 245 mm of Hg.**What is the volume at STP? 2. The volume of a gas is 65 liters at SS. What is the pressure in cm of Hg at 100.0C in a volume of 60. liters? 3. The volume of a gas is 19.0 ml at -350C and 2.51 atm. What temp. changes the volume to 20.0 ml at 3.00 atm?**PROBLEM SET ON GAS LAWS**1. A gas has a pressure of 3.14 atm at -230C. What is the pressure at 270C? 2. A gas has a volume of 56.0ml at 670.torrs. What is the volume at 800. torrs? 3. A gas has a volume of 33.0 liters at 100.0C. What temperature in Celsius changes it to 15.0 liters?**MORE OF THE SAME**4. A gas has a volume of 24.6 dl at -130C and 45.3cmHg. What is the volume at STP? 5. The molar volume of a gas at STP is 22.4 liters. What is it at SS? 6. A gas has a volume of 24.5 kl at 270C and 2.61 atm. What temperature in Celsius changes the volume to 30.0 kl at 1.00 atm?**Cole’s Law**• To one head of finely shredded cabbage, add: • 1 cup mayonaise • 1 TBSP sugar • 1 TSP vinegar • Salt and Pepper to taste**IDEAL GAS LAW**Quantity, n, temperature, T, Volume, V, and pressure, P, are all variables. a. V/T = k2 V = k2T b. P/n = k3 P = k3n Therefore,PV = (k3n)(k2T) or PV = k2k3nT k2k3 is called R, the ideal gas law constant PV = nRT**CALCULATING R**1. The molar volume of any gas is 22.4 L/mole at STP. Find R.**Values of R**• 0.0821 (liter·atm) / (mole·K) • 62.4 (liter·mm Hg) / (mole·K) • 8.32 (liter·kPa) / (mole·K)**PROBLEM SET**1. What is the volume of 18.0g of CO2 at 150C and 8.18 atm. 2. Find the temperature of 4.04 g of Ne in a volume of 10.0 liters at 45.6cm Hg. 3. What is the mass of C3H8 in 20.0 liters at 50.0C at 715mm Hg? 4. 16.0g of gas X has a volume of 13.6 liters at 250C and 1.15 atm. What is its molecular mass?**Density**Density is Mass divided by Volume D = M/V This can also be written as D•V = M O2 has a density of 1.43g/l at STP. What is its density at 1000C and .500 atm?**Density**D•V = M If the volume of a constant amount of gas is changed, the mass does not change. Thus D1•V1 = M = D2•V2 So density and volume are inversely related.**Density**Similarly we find that Density and pressure are directly related. Density and temperature are inversely related.**Density**Problem: O2 has a density of 1.43g/l at STP. What is its density at 100 0C and .500 atm? If the density of a gas is 1.25 g/l at SS, what is the density at 1000 mm Hg and 55 0C**DALTON’S LAW OF PARTIAL PRESSURE**The total pressure exerted by a mixture of gases is equal to the sum of each gas’s partial pressure. PT = P.P.s • 10.1 g Ne, 8.00g O2, and 2.80g N2 are at a total pressure of 120.mmHg. Find each gas’s partial pressure. • 16.0gO2, 2.0gH2, 8.00gCH4, and 8.0gHe are at total pressure of 4.00atm. Find each gas’s PP.**GRAHAM’S LAW OF DIFFUSION**The rate at which gaseous molecules diffuse is inversely proportional to the square roots of their molecular masses if the temperature is the same. 1. What is the relative velocity of He to CH4 at the same temperature. 2. What is the relative velocity of H2 to O2 at 250C?**3. What is the relative velocity of SO2 to HI at 1000 K?**4. Gas X moves at a relative velocity that is 2.50 times that of O2. What is the molecular mass of X? D = M D = Molar Mass V Molar Volume* *22.4 l/mole at STP and 24.5 l/mole at SS 5. Find the density of SO3 at STP and SS 6. A gas has a density of 3.45g/l at SS. What is its molecular mass?**7. What is the mass of 18.0 liters of CH4 at STP?**8. What is the mass of 18.0 liters of CH4 at 30.0C and 45.0cm of Hg? 9. What is the volume of 20.0 grams of C2H6 at SS? 10.What is the volume of 20.0 grams of C2H6 at 150C and 1.25 atm?**Density**If P1V1 = P2V2 T1 T2 and V1 = M / D1 V2 = M / D2 Then P1= P2 _ D1T1 D2 T2