CHEM 115 Chemistry - Gases PDF

CHEM 115 Chemistry Öğr Gör Sedef Özcan GASES Models for the States of Matter Gas Liquid Solid Widely separated Particles that are in Particles that are in particles in continuous contact but are able contact and unab...

CHEM 115 Chemistry Öğr Gör Sedef Özcan GASES Models for the States of Matter Gas Liquid Solid Widely separated Particles that are in Particles that are in particles in continuous contact but are able contact and unable rapid, disordered to move past each to move past one motion other another Characteristics of Gases Unlike liquids and solids, gases;  expand to fill their containers.  are highly compressible.  have extremely low densities. Physical properties of gases are all similar. Composed mainly of nonmetallic elements with simple formulas and low molar masses. Two or more gases form a homogeneous mixture. Properties Which Define the State of a Gas Sample 1) Temperature: Average velocity of the constituents of the system 2) Volume: Size of the container of the system 3) Amount of gas, usually expressed as number of moles, n. 4) Pressure: Force exerted on the walls of the container by the constituents of the system Pressure exerted by gas molecules in a box Collison of a single atom Collisions of many atoms Individual behaviour Collective behaviour No Pressure on the wall Pressure on the wall Pressure Pressure is the amount of force applied to an area: P= F A Pascals: 1 Pa = 1 N/m2 (SI unit of pressure) Bar: 1 bar = 105 Pa = 100 kPa Atmosphere: Normal atmospheric pressure at sea level is referred to as standard atmospheric pressure. 1.00 atm = 760 torr = 760 mm Hg Boyle’s Law The volume of a fixed amount of gas at constant temperature is inversely proportional to the pressure. Mathematical Relationships of Boyle’s Law  PV = a constant  This means, if we compare two conditions: P1V1 = P2V2  Also, if we make a graph of V vs. P, it will not be linear. However, a graph of V vs. 1/P will result in a linear relationship! Charles’s Law The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. Mathematical Relationships of Charles’s Law V = constant × T This means, if we compare two conditions: V1/T1 = V2/T2 Also, if we make a graph of V vs. T, it will be linear. The relationship between Kelvin temperature, T, and Celsius temperature, t, is; 0 Kelvin Avogadro’s Law The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. V = constant × n This means, if we compare two conditions: V1/n1 = V2/n2 Standard Conditions of Temperature and Pressure Because gas properties depend on temperature and pressure, it is useful to have a set of standard conditions of T and P that can be used for comparing different gases. Standard temperature: 0oC = 273 K Standard pressure: 1 atm = 760 mm Hg Also, at Standard Temperature and Pressure (STP), one mole of gas occupies 22.4 L (molar volume). At the same T, V and P samples of different gases have the same number of molecules but different masses Ideal-Gas Equation So far we’ve seen that V ∝ 1/P (Boyle’s law) V ∝ T (Charles’s law) V ∝ n (Avogadro’s law) Combining these, we get nT V∝ P Finally, to make it an equality, we use a constant of proportionality (R) and reorganize; Ideal-Gas Equation: PV = nRT Example 1 Calculate the amount of 1 L of cyclopropane gas C3H6, in moles, when measured at STP? Example 2 What is the volume occupied by 0,193 mol of Cl2 (g) at 45 oC and 745 mmHg? Dalton’s Law of Partial Pressures If two gases that don’t react are combined in a container, they act as if they are alone in the container. The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it was present alone. In other words, Ptotal = p1 + p2 + p3 + … Mole Fraction Because each gas in a mixture acts as if it is alone, we can relate amount in a mixture to partial pressures: That ratio of moles of a substance to total moles is called the mole fraction, χ. Pressure and Mole Fraction The end result is XA=14/84 = 0.167 XB=70/84 = 0.833 Example 3 What is the pressure exerted by a mixture of 0.50 mol H2 and 1.25mol He when the mixture is confined to a volume of 5L at 20oC? What are the partial pressures of H2 and He in the gaseous mixture? (H2 : 2 g/mol, He: 4 g/mol) Non-ideal (Real) Gases A useful measure of how much a gas deviates from ideal gas behavior is found in its ‘compressibility factor’. 𝑃𝑃𝑃𝑃 compressibility factor of a gas 𝑛𝑛𝑛𝑛𝑛𝑛 For an ideal gas Compressibility factor = 1 For a real gas, the compressibility factor can have values that are significantly different from 1. Non-ideal (Real) Gases All gases behave ideally at sufficiently low pressures, e.g. below 1 atm, but that deviations set in at increased pressures. At very high pressures, the compressibility factor is always greater than one Non-ideal Gas Behavior Boyle’ s law predicts that at very high pressures, a gas volume becomes extremely small and approaches zero. This cannot be, however, because the molecules themselves occupy space and are practically incompressible Non-ideal Gas Behavior i. Because of the finite size of the molecules, the PV product at high pressures is larger than predicted for an ideal gas, and the compressibility factor is greater than one. ii. Another consideration is that intermolecular forces exist in gases. Petrucci 10th Ed. Non-ideal Gas Behavior Gases tend to behave ideally at high temperatures and low pressures. Gases tend to behave non-ideally at low temperatures and high pressures. The van der Waals Equation 𝑎𝑎𝑎𝑎2 𝑃𝑃 + 2 𝑉𝑉 − 𝑛𝑛𝑛𝑛 = 𝑛𝑛𝑛𝑛𝑛𝑛 a and b are van der Waals constants 𝑉𝑉 a: a measure of how strongly the gas molecules attract one another, b: a measure of the finite volume occupied by the molecules 𝑎𝑎𝑛𝑛2 For attractive forces; 𝑉𝑉 2 𝑎𝑎𝑛𝑛2 The equation adjusts the pressure upward by adding 𝑉𝑉 2 because attractive forces between molecules tend to reduce the pressure The term nb; accounts for the small but finite volume occupied by the gas molecules; adjust the volume downward to give the volume that would be available to the molecules in the ideal case The van der Waals Equation a and b generally increase with increasing molecular mass. Larger, more massive molecules have larger volumes and tend to have greater intermolecular attractive forces Example 4 If 10.00 mol of an ideal gas were confined to 22.41 L at 0.0 °C, it would exert a pressure of 10.00 atm. Use the van der Waals equation and Table 10.3 to estimate the pressure exerted by 10.00 mol of Cl2(g) in 22.41 L at 0.0 °C. Example 5 Use the van der Waals equation to calculate the pressure exerted by 1.00 mol Cl2 (g) confined to a volume of 2.00 L at 273 K. The value of a=6.49 L2atm mol-2, and that of b=0.0562 L mol-1.