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Gases

Gases. Kinetic Theory of Gases, Gas Laws, Ideal Gases, Partial Pressures, Graham’s Law of Effusion. Characteristics of Gases. HONClBrIF: diatomic gases Noble gases are monoatomic. Many molecular compounds with low molar masses are gases at R.T.

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Gases

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  1. Gases Kinetic Theory of Gases, Gas Laws, Ideal Gases, Partial Pressures, Graham’s Law of Effusion

  2. Characteristics of Gases • HONClBrIF: diatomic gases • Noble gases are monoatomic. • Many molecular compounds with low molar masses are gases at R.T. • Gases form homogeneous mixtures regardless of gas types. • Substances that are liquids or solids at R.T. are called “vapors”. Ex: water vapor

  3. Kinetic-Molecular Theory of Gases • A gas is composed of particles (molecules or atoms). • Gas particles are considered to be small, hard spheres (billiard balls). • Particles have insignificant volume compared to total volume occupied by the gas. • Particles are far apart from each other. • Between the particles is empty space.

  4. Kinetic Theory of Gases, Cont. • No attractive or repulsive forces exist between particles. • Particles move rapidly in constant random motion (random walk). • Movement is independent; particles travel in straight paths until a collision. • Collisions between gas particles are perfectly elastic. (Newton’s Cradle). This is true at constant temperature and low to moderate pressure.

  5. Kinetic Theory of Gases, Part III • Average kinetic energy (EK) of a gas molecule is proportional to the absolute temperature (K). If K doubles, EK doubles. • At any given temperature, all gases have the same average EK. • At a fixed temperature, the average speed of a lighter gas is greater than the average speed of a heavier gas.

  6. Pressure • Gas pressure: the force exerted by a gas per unit surface area of an object. • P = F/A • Gas pressure is the result of simultaneous collisions of billions of rapidly-moving particles with an object. • Vacuum: no gas particles, no pressure

  7. Atmospheric Pressure: the collision of air molecules with objects.

  8. Atmospheric Pressure

  9. Units of Pressure • SI Unit is the pascal (Pa); kPa is used more frequently. • Other units include: mmHg, bar, torr, psi, atmosphere (atm) • 1 atm = 760 mmHg = 760 torr = 101.3 kPa • A barometer measures air pressure.

  10. Standard Atmospheric Pressure (STP) • STP is the typical pressure at sea level • STP is the pressure needed to support a column of mercury 760 mm high. • STP for a gas is 0°C and 1 atm.

  11. The Manometer • A manometer is sometimes used in the laboratory to measure gas pressures near atmospheric pressure. • Operates on a principle similar to that of a barometer. • Interesting fact: a blood pressure cuff is a sphygmomanometer.

  12. A Manometer Calculation • A gas sample is in a flask attached to an open-end manometer in a room with atmospheric pressure of 764.7 torr. The mercury level in the open-arm end of the manometer has a height of 136.4mm, and that is the arm in contact with the gas has a height of 103.8mm. What is the gas pressure in atm?

  13. Solution to Manometer Calculation • Pressure of gas > atmospheric pressure. (How do we know this?) • Pgas = Patm + Ph • The gas pressure equals the atmospheric pressure plus the difference in height between the two manometer arms. • Pgas = 764.7 torr + (136.4 torr - 103.8 torr) = 797.3 torr = 1.049 atm

  14. The Gas Laws • Four variables are needed to define the condition of a gas: • Temperature (T), always in K • Pressure (P), in various units (kPa, atm) • Volume (V), usually L or mL • Number of gas moles (n), in mol • The gas laws describe the relationships between these variables.

  15. Boyle’s Law, 1662 • Pressure-Volume Relationship • At constant n and T, P 1/V or PV = constant as P, V • For use in calculations, P1V1 = P2V2 • Example of Boyle’s Law: breathing

  16. Boyle’s Law Graph: Volume vs. Pressure

  17. A Boyle’s Law Calculation • A fixed quantity of gas at 23.0C has a pressure of 748 torr and occupies a volume of 10.3 L. Calculate the volume (L) if the pressure increases to 1.88 atm and the temperature remains constant. • 5.39 L

  18. Another Boyle’s Law Calculation • A gas with a volume of 4.0 L at 90.0 kPa expands until the pressure drops to 20.0 kPa. What is the new volume if the temperature doesn’t change? • 18 L

  19. Charles’ Law, 1787 • Temperature-Volume relationship • At constant n and P: T V as T, V • For use in calculations, V1/T1 = V2/T2

  20. Charles’ Law Graphs: Volume vs. Temperature

  21. Charles’ Law and Kelvin Scale • We get a straight-line graph of Charles’ Law data. • Zero volume equals -273.15C. • Lord Kelvin creates the absolute scale where 0K = -273.15C. • WE MUST USE KELVIN SCALE FOR CHARLES’ LAW CALCS!

  22. A Charles’ Law Calculation • We have a fixed quantity of gas at 23.0C and a pressure of 748 torr. The gas volume is 10.3 L. If the temperature rises to 165.0C, what will the new volume be if the gas pressure remains constant? • Volume = 15.2 L

  23. Another Charles’ Law Calculation • A gas with a volume of 300. mL at 150.0C is heated until its volume is 600. mL. What is the new temperature of the gas if the pressure remains constant during the heating process? • 846 K

  24. Gay-Lussac’s Law, 1802 • Temperature-Pressure relationship • At constant n and V, TP as T, P • Temperature must be in Kelvin • For use in calculations, P1/T1 = P2/T2 Example: pressure cooker

  25. A Gay-Lussac’s Law Calculation • The gas in a used aerosol can is at a pressure of 103 kPa at 25.0C. If David throws the can into a fire, what will the gas pressure be when the temperature reaches 928.0C? • Pressure = 415 kPa

  26. Another Gay-Lussac Calculation • A sealed cylinder contains nitrogen gas at 1.00 x 103 kPa pressure and a temperature of 20.0C. When the cylinder is left in the sun, the temperature rises by thirty degrees. What is the new gas pressure in kPa? • 1.10 x 103 kPa

  27. Avogadro’s Law • Mole-Volume relationship • At constant T and P: n V as n,V • In other words, doubling the moles of a gas will cause V to double if P and T are held constant.

  28. Molar Volume of a Gas • Avogadro’s Hypothesis: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. • Molar Volume of a Gas: At STP, 1 mole of any gas = 22.4L = 6.02 x 1023 particles

  29. Combined Gas Law • At constant n, P1V1/T1 = P2V2 /T2 Calculation: The volume of a gas-filled balloon is 30.0 L at 313 K and 153 kPa. What would the volume be at STP? 39.5 L

  30. Another Combined Gas Law Calculation • A gas at 155 kPa and 25.0C has an initial volume of 1.00 L. If the pressure increases to 605 kPa and the volume decreases to 0.342 L, what is the final temperature of the gas in Kelvin? • 398 K

  31. Ideal Gas Law • PV = nRT • P = pressure (various units) V = volume (L) n = number of gas moles (mol) T = temperature (K only) R = ideal gas constant. R has many units. Most common: 8.314 L• kPa/mol•K and 0.0821 L•atm/mol•k

  32. Ideal Gas Law, Cont. • A gas that obeys this equation is said to behave ideally. • This law accounts for the properties of most gases under a wide variety of circumstances. • This law works best for gases at low pressure and high temperature.

  33. An Ideal Gas Law Calculation • A deep underground cavern contains 2.24 x 106 L of methane gas at a pressure of 1.50 x 103 kPa and a temperature of 315 K. How many kg of CH4 does the cavern contain? • 2.06 x 104 kg methane

  34. Another Gas Law Calculation • A rigid hollow sphere contains 251 mol of He gas at a temperature of 621K and a pressure of 1.89 x 103 kPa. How many liters of gas are in the sphere? • 686 L

  35. Yet Another Ideal Gas Law Calculation • If 4.50 g of methane gas (CH4) are in a 2.00-L container at 35.0C, what is the pressure in the container (atm)? • 3.55 atm

  36. Real Gas Deviation from Ideal Behavior • Ideal Gas Law is useful, but all real gases fail to obey it to some degree. • At high pressures, real gases do not behave ideally. • The deviation from ideal behavior is small at lower pressures (below 10 atm).

  37. Deviations from Ideal Gas Law, Cont. • As temperature increases, a gas acts more ideally. • The deviations from ideal behavior increase as temperature decreases, becoming significant near the temperature at which the gas is converted to a liquid.

  38. Why Don’t Real Gases Behave Ideally?…Volume • Contrary to the Kinetic-Molecular Theory, real gases do have finite volumes. • At low pressure, gas volume is negligible compared with the container volume. Gas particles move freely. • At higher pressures, the volume of the gas particles is a larger fraction of the total space available. Free space is more limited. Gas volumes are greater than those predicted by the Ideal Gas Law.

  39. Why Don’t Real Gases Behave Ideally?…Attractive Forces • Contrary to the K-M Theory, real gases particles are attracted to each other. • At high pressure, particles experience more attraction because they are closer together. • As temperature decreases, gas particles move slower and experience more attraction. • More attraction = more deviation from ideal behavior.

  40. The van der Waals Equation • Correction of Ideal Gas Law. • P = (nRT/V-nb) - (n2a/V2) where nb corrects for volume and n2a/V2 corrects for molecular attraction. • Another form of van der Waals: [P + (n2a/V2)](V-nb) = nRT

  41. A van der Waals Calculation • Use the van der Waals equation to estimate the pressure (atm) exerted by 1.000 mol of chlorine gas in 22.41L at 0.0C. The needed constants a and b are on page 395 in your book. • 0.990 atm (For an ideal gas, the pressure would be 1.000 atm.)

  42. Another van der Waals Calculation • Consider a sample of 1.000 mol of carbon dioxide gas confined to a volume of 3.000 L at 0.0C. Calculate the pressure using the ideal gas equation and the van der Waals equation. • Ideal gas: 7.473 atm Real gas: 7.182 atm

  43. Gas Densities and Molar Mass • Ideal Gas equation can be used to measure and calculate gas density. • Gas densities in g/L. • Rearrange equation: n/V = P/RT • Multiply both sides by M = molar mass (g/mol) • nM/V = PM/RT • So…density of a gas equals: d = PM/RT

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