Chapter 5 Handouts(1)

# Chapter 5 Handouts(1) - Chapter 5 – Gases The Structure...

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Unformatted text preview: Chapter 5 – Gases The Structure of a Gas •  Gases are composed of particles that are flying around very fast in their container •  T he particles in straight lines until they encounter either the container wall or another particle, then they bounce off •  As they move and strike a surface, they push on that surface !  push = force = pressure Pressure = Force/ area Physical Characteristics of Gases •  •  Gases assume the volume and shape of their containers. Gases are the most compressible state of matter •  Gases will mix evenly and completely when confined to the same container. •  Gases have much lower densities than liquids and solids. •  Density is measure as g/L The Pressure of a Gas •  The pressure of a gas depends on several factors !  number of gas particles in a given volume !  volume of the container !  average speed of the gas particles Measuring Air Pressure Force Pressure = Area (force = mass x acceleration) Units of Pressure 1 pascal (Pa) = 1 N/m2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa = 14.7 psi gravity Example 5.1: A high-performance bicycle tire has a pressure of 132 psi. What is the pressure in mmHg? Given: Find: Conceptual Plan: Relationships: Solution: Check: psi to atm to mmHg 1atm= 14.7 psi, 1atm = 760 mmHg Manometer for this sample, the gas has a large pressure than the atmosphere Boyle’s Law Robert Boyle (1627–1691) 100 mL 90 mL 50 mL A P (h) increses, V decreases 30 mL Boyle’s Law P P P Volume decreases Volume increases (Pressure increases) (Pressure decreases) Boyle’s Law Constant temperature Constant amount of gas Boyle’s Law: A Molecular View •  Pressure is caused by the molecules striking the sides of the container •  When you DECREASE THE VOLUME of the container with the same number of molecules in the container, more molecules will hit the wall at the same instant •  This results in increasing the pressure A balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2.78x 103 mL, what was it originally? Given: Find: Conceptual Plan: Relationships: Solution: Check: Charles’s Law Pressure and n are constant As T increases, V increases Heating or cooling a gas at constant pressure P P P Lower temperature Higher temperature (Volume decreases) (Volume increases) Heating or cooling a gas at constant volume P Charles’s Law P P Lower temperature Higher temperature (Pressure decreases) (Pressure increases) P1 P2 P3 P4 Charles’ & Gay-Lussac’s Law P!T P = constant x T P1/T1 = P2/T2 V and T are directly proportional V=constant x T V1IT = V2IT2 Temperature must be in Kelvin T (K) = t (0C) + 273.15 Example 5.3: A gas has a volume of 2.57 L at 0.00 °C. What was the temperature at 2.80 L? Given: Find: Conceptual Plan: Relationships: Solution: Check: Avogadro’s Law V is proportional to the number of moles (n) V + constant x n V1In1=V2In2 If they have the same pressure and temp, 1 mole has the same volume no matter what gas it is Constant temperature Constant pressure Ideal Gas Law Boyle’s law: V ! 1 (at constant n and T)" P Charles’ law: V ! T (at constant n and P)" Avogadro’s law: V ! n (at constant P and T)" V! nT P nT nT V = constant x =R P P R is the gas constant 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. Ideal Gas Molecules neither attract or repel one another The volume of the molecule is negligible PV = nRT R= PV/nT = (1atm)(22.414L)/ 1(mol0(273.15 k) R= .082057 L * atm/ (mol*K) Example 5.6: How many moles of gas are in a basketball with total pressure 24.3 psi, volume of 3.24 L at 25°C? Given: Find: Conceptual Plan: Relationships: Solution: Check: A gas occupies 10.0 L at 44.1 psi and 27 °C. What volume will it occupy at standard conditions? Given: Find: Conceptual Plan: Relationships: Solution: Check: Practice—Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 x 104 mmHg and –23 °C. Given: Find: Conceptual Plan: Relationships: Solution: Molar Volume •  Solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L !  6.022 x 1023 gas molecules •  We call the volume of 1 mole of gas at STP the molar volume !  it is important to recognize that one mole measures of different gases have different masses, even though they have the same volume Practice — How many liters of O2 @ STP can be made from the decomposition of 100.0 g of PbO2? 2 PbO2(s) ! 2 PbO(s) + O2(g) Given: Find: Conceptual Plan: Relationships: Solution: Check: Density at Standard Conditions Density (d) Calculations d=(m/v) = (PMM/RT), m is the mass of the gas in g, MM is the molar mass of the gas Molar Mass (MM) of a Gaseous Substance dRT MM = P d is the density of the gas in g/L Example 5.7: Calculate the density of N2 at 125°C and 755 mmHg Given: Find: Conceptual Plan: Relationships: Solution: Check: Example 5.8: Calculate the molar mass of a gas with mass 0.311 g that has a volume of 0.225 L at 55°C and 886 mmHg Given: Find: Conceptual Plan: Relationships: Solution: Check: Mixtures of Gases •  When gases are mixed together, their molecules behave independent of each other V and T are constant P total= P1 + P2 Consider a case in which two gases, A and B, are in a container of volume V. nART PA = V nA is the number of moles of A nBRT PB = V nB is the number of moles of B PT = PA + PB PA = XA PT nA XA = nA + nB nB XB = nA + nB PB = XB PT P(i) = x(i)P(T) mole fraction (xi)= ni/nT Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe Given: Find: Conceptual Plan: Relationships: Solution: Check: Find the mole fraction of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe Given: Find: Conceptual Plan: Relationships: Solution: Check: Reactions Involving Gases •  The principles of reaction stoichiometry from Chapter 4 can be combined with the gas laws •  In reactions of gases, the amount of a gas is often given as a volume •  T he ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefﬁcients in the equation as a mole ratio P, V, T of Gas A mole A mole B P, V, T of Gas B Ex 5.12: What volume of H2 is needed to make 35.7 g of CH3OH at 738 mmHg and 355 K? CO(g) + 2 H2(g) ! CH3OH(g) Given: Find: Conceptual Plan: Relationships: Solution: Ex 5.13: How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP? O2(g) + 2 H2(g) ! 2 H2O(g) Given: Find: Concept Plan: Relationships: Solution: Kinetic Molecular Theory 1.  A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is,. they posses mass but have negligible volume 2.  Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic. 3.  Gas molecules exert neither attractive nor repulsive forces on one another. 4.  The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy Kinetic Molecular Theory •  There is a lot of empty space between the gas particles ! compared to the size of the particles •  The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature !  as you raise the temperature of the gas, the average speed of the particles increses " but don’t be fooled into thinking all the gas particles are moving at the same speed!! Kinetic theory of gases and … •  Compressibility of Gases •  Boyle’s Law directly proportional P ! collision rate with wall Collision rate ! number density Number density ! 1/V P ! 1/V •  Charles’ Law P ! collision rate with wall Collision rate ! average kinetic energy of gas molecules Average kinetic energy ! T P!T Kinetic theory of gases and … •  Avogadro’s Law P ! collision rate with wall Collision rate ! number density Number density ! n P!n •  Dalton’s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas Ptotal = #Pi Kinetic Energy and Molecular Velocities •  Average kinetic energy of the gas molecules depends on the average mass and velocity ! KE = "mv2 •  Gases in the same container have the same temperature, therefore they have the same average kinetic energy •  If they have different masses, the only way for them to have the same kinetic energy is to have different average velocities ! lighter particles will have a faster average velocity than more massive particles U(rms @ T U(rms) @ 1/ M The distribution of speeds of three different gases at the same temperature The distribution of speeds for nitrogen gas molecules at three different temperatures U(rms)= sqrt(3RT/MM) MM=kg/mol R= 8.314 J/M mol 5.7 Ex 5.14: Calculate the rms velocity of O2 at 25 °C Given: Find: Conceptual Plan: Relationships: Solution: Practice – Calculate the rms velocity of CH4 at 25 °C Given: Find: Conceptual Plan: Relationships: Solution: Mean Free Path •  Molecules in a gas travel in straight lines until they collide with another molecule or the container •  The average distance a molecule travels between collisions is called the mean free path •  Mean free path decreases as the pressure increases Gas diffusion is the gradual mixing of molecules of one gas with mlecules of another by virtue of their kinetic properties NH3 + HCl NH4Cl NH4Cl # r1 = r2 M2 M1 N H3 17 g/mol HCl 36 g/mol Gas effusion is the process by which a gas under pressure escapes from one compartment of a container to another by passing through a small opening Ex 5.15: Calculate the molar mass of a gas that effuses at a rate 0.462 times N2 Given: Find: Conceptual Plan: Relationships: Solution: Ideal vs. Real Gases 1 mole of ideal gas: PV = nRT n= PV/RT = 1.0 Real Gas Behavior •  real molecules take up space - the molar volume of a gas is larger than predicted by the ideal gas law at high pressures •  real molecules attract each other - the molar volume of a gas is smaller than predicted by the ideal gas law at low temperatures When do gases become real? Intermolecular forces Attractive forces Repulsive forces Real Gas Equation: P(ideal)= P(real) + an2N2 van der Waals’ Equation •  Combining the equations to account for molecular volume and intermolecular attractions we get the following equation ! used for real gases (P+a(n/v)2)*(V-nb)=nRT ...
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## This note was uploaded on 02/01/2012 for the course CHEM 105 taught by Professor Woodrum during the Fall '08 term at Kentucky.

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