Chapter 02 Gases

Mercury barometer

A mercury barometer is used to measure atmospheric pressure by determining the height of a mercury column supported in a sealed glass tube. The downward pressure of the mercury in the column is exactly balanced by the outside atmospheric pressure that presses down on the mercury in the 1 dish and pushes it up the column.

Open-end manometer

The pressure in the bulb is lower than atmospheric, so the mercury level is higher in the arm open to the bulb.

The pressure in the bulb is higher than atmospheric, so the mercury level is higher in the arm open to the atmosphere.

Open-end manometers for measuring pressure in a gas-filled bulb 2

Gas Pressure Units Gas pressure is the collisions of randomly moving particles with the walls of the container exert a force per unit area. SI Units of pressure: atmosphere (atm) Other units: 1 atm = 760 mm Hg = 760 torr (1 mm Hg = 1 torr) 1 atm = 101325 Pa = 101.3 kPa (1 Pa = 1 N/m2) 1 atm = 1.01325 bar 1 atm = 29.921 in Hg 1 atm = 14.7 lb/in2 1 atm = psi 3

The Gas Laws The physical properties of any gas can be described completely (more or less) by four variables: The specific relationships among these four variables are the gas laws, and a gas whose behavior follows these laws exactly is called an ideal gas. There are four key gas law equations that have been empirically determined, which are combined into the combined gas law and the ideal gas law.

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Boyle’s Law: Pressure and Volume Pressure–Volume Law: • The volume of a fixed amount of gas maintained at constant temperature is inversely proportional to the gas pressure. As the volume of the gas decreases, the gas particles have less room to move around in, and they collide more often with the walls of the container, thus increasing the pressure.

(n, T constant)

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Charles’ Law: Temperature and Volume Temperature–Volume Law: • The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin temperature of the gas (not the Celsius temp!) • If the absolute temperature is doubled, the volume is doubled.

V  T (n,P constant) 6

Avogadro’s Law: Volume and Amount The Volume–Amount Law: • At constant pressure and temperature, the volume of a gas is directly proportional to the number of moles of the gas present.

(P,T constant) 7

Gay-Lussac’s Law: Pressure and Temperature

For a fixed amount of gas at a constant volume, the pressure of a gas is directly proportional to its Kelvin temperature.

P  T

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Combined Gas Law Since PV, V/T and P/T all have constant values for fixed amount of gas, these relationships can be merged into a combined gas law, which holds true whenever the amount of gas is fixed.

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The Ideal Gas Law

Ideal gases obey an equation incorporating the laws of Charles, Boyle, and Avogadro.

1 mole of an ideal gas occupies 22.414 L at STP STP conditions are 273.15 K and 1 atm pressure R is a proportionality constant called the ideal gas constant, which has the same value for all gases: R = 0.08206 L·atm·K–1mol–1 R = 8.314 JK-1mol-1 R = 62.36 L torr K-1 mol-1

(if P = atm, V = L) (if P = Pa, V = m3) (if P = torr, V = L) 10

The Ideal Gas Law • Density and Molar Mass Calculations:

• You can calculate the density or molar mass (M) of a gas. The density of a gas is usually very low under atmospheric conditions.

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Stoichiometric Relationships with Gases • We can now combine gas law problems with stoichiometry problems. • For instance, if we know the temperature, volume, and pressure of a gas reactant or product, we can calculate the amount (mol) from the ideal gas law, and use the coefficients of the balanced equation to convert that into moles of another reactant or product P,V,T of gas A

amount A (in moles)

amount B (in moles)

P,V,T of gas B 12

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Dalton’s Law of Partial The total pressurePressures exerted by a mixture of gases in a container at constant V and T is equal to the sum of the partial pressures exerted by each individual gas in the container Ptotal = P1 + P2 + P3 + …..

Dalton’s law allows us to work with mixtures of gases. 13

Dalton’s Law of Partial Pressures

• For a two-component system, the moles of components A and B can be represented by the mole fractions (XA and XB).

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Dalton’s Law of Partial Pressures

• Mole fraction is related to the total pressure by:

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Kinetic Molecular Theory of • This theory presents physical Gases properties of gases in terms of the motion of individual molecules. • The kinetic-molecular theory is based on the following assumptions: 1. A gas consists of tiny particles, either atoms or molecules, constantly moving about in straight lines until they collide with another particle or the wall of the container. 2. The size of the gas particles is negligibly small compared to the total volume of the gas. Most of the volume of a gas is empty space. 16

Kinetic Molecular Theory of Gases 3.The average kinetic energy of the gas particles is directly proportional to the temperature of the gas in Kelvin. There is a distribution of velocities in a sample of gas — some particles are moving faster and some are moving slower — but the higher the temperature, the greater the average kinetic energy is. (EK = ½mv2)

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Kinetic Molecular Theory of Gases 4.The collisions of particles with each other or with the walls of the container are completely elastic. When the particles collide, they may exchange energy, but there is no overall loss of energy: the total kinetic energy of the gas particles is constant at constant T. The gas particles do not attract each other, so there is no “stickiness” to the particles.

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Gas law summary

(a) (b) (c) (d)

Decreasing the volume of the gas at constant n and T increases the frequency of collisions with the container walls and therefore increases the pressure (Boyle’s law). Increasing the temperature (kinetic energy) at constant n and P increases the volume of the gas (Charles’ law). Increasing the amount of gas at constant T and P increases the volume (Avogadro’s law). Changing the identity of some gas molecules at constant T and V has no effect on the pressure (Dalton’s law). 19

Behavior of Real Gases

• Real gases are gases that deviate from “ideal gas law” but under most conditions, these deviations are slight. • The actual molar volumes of real gases are not exactly 22.4 L, but they are fairly close (more later).

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Behavior of Real Gases The behavior of real gases is often quite a bit different from that of ideal gases, especially at very low temperatures or very high pressures. Ideal gases assumptions Molecules in gaseous state do not exert any force, either attractive or repulsive, on one another. Volume of the molecules is negligibly small compared with that of the container.

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Behavior of Real Gases •

However, at higher pressures, particles are much closer together and attractive forces become more important.

Molecules attract one another at distances up to about 10 molecular diameters. The result of the attraction is a decrease in the actual volume of most real gases when compared with ideal gases at pressures up to 300 atm. 22

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Behavior of Real Gases

The volume taken up by gas particles is actually less important at lower pressures than at higher pressure. As a result, the volume at high pressure will be greater than the ideal value.

The volume taken up by the gas particles themselves is less important at lower pressure (a) than at higher pressure (b). As a result, the volume of a real gas at high pressure is somewhat larger than the ideal value

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Behavior of Real Gases Corrections for non-ideality require van der Waals equation.

Correction for intermolecular attractions

Correction for gas particle volume

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