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## Gases

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**Gases**Chapter 10**Characteristics of Gases**• Expand to fill a volume (expandability) • Compressible • Readily forms homogeneous mixtures with other gases • Have extremely low densities. • These behaviors are due to large distances between the gas molecules.**F**A P = Pressure • Pressure is the amount of force applied to an area. • Atmospheric pressure is the weight of air per unit of area.**Units of Pressure**• Pascals • 1 Pa = 1 N/m2 • Bar • 1 bar = 105 Pa = 100 kPa • mm Hg or torr • These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury. • Atmosphere • 1.00 atm = 760 torr**Pressure**• Conversion Factors • 1 atm = 760 mmHg • 1 atm = 760 torr • 1 atm = 1.01325 105 Pa • 1 atm = 101.325 kPa.**Manometer**Used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel. Manometer at <, =, > P of 1 atm**Example**• On a certain day the barometer in a laboratory indicates that the atmospheric pressure is 764.7 torr. A sample of gas is placed in a vessel attached to an open-end mercury manometer. A meter stick is used to measure the height of the mercury above the bottom of the manometer. Level of the mercury in the open end arm of the manometer has a measured height of 136.4 mm, and that in the arm that is in contact with the gas has a height of 103.8 mm. • What is the pressure of the gas? • What is the pressure of the gas in kPa**The Gas Laws**• There are four variables required to describe a gas: • Amount of substance • Volume of substance • Pressures of substance • Temperature of substance • The gas laws will hold two of the variables constant and see how the other two vary.**Boyle’s Law**The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.**PV = k**• Since • V = k (1/P) • This means a plot of V versus 1/P will be a straight line. As P and V areinversely proportional A plot of V versus P results in a curve.**A sample of chlorine gas occupies a volume of 946 mL at a**pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?**V**T = k • i.e., Charles’s Law • The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. A plot of V versus T will be a straight line.**A sample of carbon monoxide gas occupies 3.20 L at 125 0C.**At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?**V = kn**• Mathematically, this means Avogadro’s Law • The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.**Ammonia burns in oxygen to form nitric oxide (NO) and water**vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?**Combining these, we get**nT P V Ideal-Gas Equation V 1/P (Boyle’s law) VT (Charles’s law) Vn (Avogadro’s law) • So far we’ve seen that**The Ideal Gas Equation**• Combine the gas laws (Boyle, Charles, Avogadro) yields a new law or equation. • Ideal gas equation: • PV = nRT • R = gas constant = 0.08206 L.atm/mol-K • P = pressure (atm) V = volume (L) • n = moles T = temperature (K)**The conditions 0 0C and 1 atm are called standard**temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L. R = 0.082057 L • atm / (mol • K)**What is the volume (in liters) occupied by 49.8 g of HCl at**STP?**Argon is an inert gas used in lightbulbs to retard the**vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?**n**V P RT = Densities of Gases If we divide both sides of the ideal-gas equation by V and by RT, we get**m**V P RT = Densities of Gases • We know that • moles molecular mass = mass n = m • So multiplying both sides by the molecular mass ( ) gives**m**V P RT d = = Densities of Gases • Mass volume = density • So, • Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.**P**RT dRT P d = = Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: Becomes**What is the volume of CO2 produced at 370 C and 1.00 atm**when 5.60 g of glucose are used up in the reaction: C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l) Gas Stoichiometry**Gas Mixtures and Partial Pressures**Dalton’s Law Dalton’s Law - In a gas mixture the total pressure is given by the sum of partial pressures of each component: Pt = P1 + P2 + P3 + … - The pressure due to an individual gas is called a partial pressure.**PA =**nART nBRT V V PB = nA nB nA + nB nA + nB XA = XB = Consider a case in which two gases, A and B, are in a container of volume V. nA is the number of moles of A nB is the number of moles of B PT = PA + PB PA = XAPT PB = XBPT Pi = XiPT where i is the mole fraction (ni/nt).**A sample of natural gas contains 8.24 moles of CH4, 0.421**moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?**Partial Pressures**• When one collects a gas over water, there is water vapor mixed in with the gas. • To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.**Kinetic-Molecular Theory**This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.**Kinetic-Molecular Theory**• Theory developed to explain gas behavior • To describe the behavior of a gas, we must first describe what a gas is: • Gases consist of a large number of molecules in constant random motion. • Volume of individual molecules negligible compared to volume of container.**Kinetic-Molecular Theory**• Intermolecular forces (forces between gas molecules) negligible. • Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. • Average kinetic energy of molecules is proportional to temperature.**Kinetic-Molecular Theory**ε = ½ mu2**Application to the Gas laws**• Effect of Volume increase at constant temperature • More space • Fewer collisions • u is unchanged • Effect of a temperature increase at constant volume • Less Space • More collisions • Increase in u**Molecular Effusion and Diffusion**• Consider two gases at the same temperature: the lighter gas has a higher u than the heavier gas. • Mathematically: • The lower the molar mass, M, the higher the u for that gas at a constant temperature.**Effusion**The escape of gas molecules through a tiny hole into an evacuated space.**NH4Cl**Diffusion The spread of one substance throughout a space or throughout a second substance. NH3 17 g/mol HCl 36 g/mol**Molecular Effusion and Diffusion**Graham’s Law of Effusion • Graham’s Law of Effusion – The rate of effusion of a gas is inversely proportional to the square root of its molecular mass. • Gas escaping from a balloon is a good example.**Molecular Effusion and Diffusion**Diffusion and Mean Free Path • Diffusion of a gas is the spread of the gas through space. • Diffusion is faster for light gas molecules. • Diffusion is slowed by gas molecules colliding with each other. • Average distance of a gas molecule between collisions is called mean free path.**Real Gases**In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.**Real Gases: Deviations from Ideal Behavior**• From the ideal gas equation, we have PV = nRT • This equation breaks-down at • High pressure • At high pressure, the attractive and repulsive forces between gas molecules becomes significant. • Small volume • At small volumes, the volume due to the gas molecules is a source of error.**Deviations from Ideal Behavior**The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature.**Corrections for Nonideal Behavior**• The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account. • The corrected ideal-gas equation is known as the van der Waals equation.**Real Gases: Deviations from Ideal Behavior**The Van der Waals Equation • Two terms are added to the ideal gas equation to correct for volume of molecules and one to correct for intermolecular attractions. • a and b are constants, determined by the particular gas.**(P +**) (V−nb) = nRT n2a V2 The van der Waals Equation**Example**• Consider a sample of 1.00 mol of carbon dioxide gas confined to a volume of 3.000L at 0.0 C. Calculate the pressure of the gas using the van der waals equation