Pressure is defined as a force applied over a unit area. Pressures increases when the applied force increases or the area over which it is applied decreases.

The weight of the atmosphere pressing against the Earth’s surface is called atmospheric pressure. The weight is due to the gravitational attraction between the Earth and the nitrogen, oxygen, and other gases in the atmosphere. The atmosphere is about 79% nitrogen, 20% oxygen and 1% other gases such as water vapor. Atmospheric pressure increases under cold air (more dense) and decreases under hot air (less dense). Atmospheric pressure also decreases with increasing elevation. The actual force of the atmosphere pushing on a surface arises from individual rapidly moving gas molecules in the atmosphere bouncing off the surface.

Atmospheric pressure is measured by an instrument called a barometer. One type of barometer, the mercury barometer, measures atmospheric pressure by the height of the column of mercury it will support: One standard atmosphere is defined as the pressure that will support a column of mercury of height 760 mm at 0o C. Pressure can be expressed in atmospheres, mm Hg, or torr (the same as 1 mm Hg). 1 atm = 14.6 lb/ft2 = 760 torr = 760 mm Hg

The pressure of gas in a closed container is measured by a device called a manometer. The difference in the height of the mercury column (mm Hg or torr) in the two arms of the manometer represents the difference in pressure between atmospheric pressure and the pressure of the gas sample.

When the mercury in the arm of the manometer connected to the gas sample is lower than in the other arm, the pressure of the gas sample is greater than atmospheric pressure by the difference in heights. A more practical manometer for everyday use involves a membrane or diaphram separating the gas from a springlike mechanical device which is calibrated to read the pressure in pounds per square inch or millimeters of mercury.

The physical properties of a gas depends upon only four variables: Pressure (P) Volume (V) Number of moles (n) Kelvin temperature (T) Pressure and Temperature • Pressure = force/area (we will use torr, mm Hg, Pa & atm) • Always use Kelvin temperature (K) K = ° C + 273

A group of laws, each of which involve only two of the four variables, have names based on their discoverers: To examine these laws we will use an imaginary system consisting of a cylinder with a movable piston. The temperature of the gas in the cylinder can be held constant (room temperature) by allowing heat to flow across the cylinder wall.

The number of moles and temperature of a gas sample are held constant The number of moles and temperature of a gas sample are held constant. The volume is allowed to vary as the external pressure applied to the gas sample is varied.

Increasing the pressure on the gas in the cylinder causes the volume of the gas to decrease. This could also be stated: decreasing the volume of the gas in the cylinder causes the pressure to increase. A gas consists of a very large number of molecules moving randomly within its container. Decreasing the volume of the container will increase the frequency that gas molecules collide with the walls of the container (less room to move about), thus increasing the pressure. The experimental data above can be summarized mathematically: P x V = constant or P1V1 = P2V2 = P3V3 = …

The mathematical representation of Boyles Law can be interpreted in two different ways to solve two different types of problem: P2V2 = P1V1 Given a starting volume and pressure, calculate the new volume given a new pressure at constant n and T. V2 = V1 * (P1/P2) Given a starting volume and pressure, calculate the new pressure given a new volume at constant n and T. P2 = P1 * (V1/V2)

The Pressure-Volume Relationship: Boyle’s Law If temperature T and amount of gas n does not change, pressure P is inversely proportional to volume V. P a 1/V P x V = constant P1 x V1 = P2 x V2

Charles’s Law relates the volume and temperature of a sample of gas when the pressure and number of moles of gas are held constant.

The experimental data above can be mathematically interpreted: V/T = constant or V1/T1 = V2/T2 = V3/T3 = …

As with Boyle’s Law, Charles Law can be rewritten to solve two types of problems: V2/T2 = V1/T1 Given a starting volume and temperature, calculate the new volume if the temperature is changed at constant n and P. V2 = V1 * (T2/T1) Given a starting volume and temperature, calculate the new temperature if the volume is changed at constant n and P. T2 = T1 * (V2/V1)

Gay-Lussac’s Law relates the pressure and temperature of a gas when the volume and number of moles are held constant.

The experimental data above can be interpreted mathematically: P/T = constant or P1/T1 = P2/T2 = P3/T3 = …

Gay-Lussac’s Law can also be written to solve two types of problems: P2/T2 = P1/T1 Given a starting pressure and temperature, calculate the new pressure when the temperature changes at constant n and V. P2 = P1 * (T2/T1) Given a starting pressure and temperature, calculate the new temperature when the pressure changes at constant n and V. T2 = T1 * (P2/P1)

Avogadro’s Law relates the volume of a gas to the number of moles of gas present when the pressure and temperature are held constant.

The experimental data above can be expressed mathematically: V/n = constant or V1/n1 = V2/n2 = V3/n3 = …

Avogadro’s Law can again be written in two different ways to solve two different types of problems: V2/n2 = V1/n1 Given the volume and number of moles of gas present, calculate the new volume if the number of moles changes at constant T and P: V2 = V1 * (n2/n1) Given the volume and number of moles of gas present, calculate the new number of moles present when the volume changes at constant T and P: n2 = n1 * (V2/V1)

The Volume-amount Relationship: Avogadro’s Law If P and T do NOT change, then n is proportional to V V a number of moles (n) V = constant x n V1 / n1 = V2 / n2

4NH3 + 5O2 4NO + 6H2O 1 mole NH3 1 mole NO At constant T and P 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? 4NH3 + 5O2 4NO + 6H2O 1 mole NH3 1 mole NO At constant T and P 1 volume NH3 1 volume NO 5.3

Ideal Gas Equation 1 Boyle’s law: V a (at constant n and T) P Charles’ law: V a T (at constant n and P) Avogadro’s law: V a n (at constant P and T) V a nT P V = constant x = R nT P R is the gas constant PV = nRT Ideal gas is a hypothetical gas whose pressure-volume-temperature behavior can be completely accounted for by the ideal gas equation.

All four variables, P, V, n, and T, can be combined into the following single mathematical expression called the ideal gas law. PV/nT = constant = R, where R is the universal gas constant. The ideal gas law is usually written: PV = nRT All gases at room temperature and pressure follow this law closely.

The value of R can be determined by measuring all four variables for a sample of gas. It has been determined that 1 mole of a gas at 1.00 atm pressure (760 torr) and 273 K always occupies 22.4 L. The value of R will subsequently be written 0.0821 L·atm·mol-1·K-1. As for the other laws, the ideal gas law can be rewritten as: P2V2/n2T2 = P1V1/n1T1 and rearranged to find the new value of one of the variables when the other three change simultaneously. For instance: V2 = V1 * (P1/P2) * (n2/n1) * (T2/T1)

In calculation, the units of R must match those for P,V,T and n. 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. Molar volume of gas • 1 mole of gas at STP = 22.4 Liters • Example: 2 moles of gas at STP = 44.8 L PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)(273.15 K) R = 0.082057 L • atm / (mol • K)=8.314J/(K·mol) = 8.314 L·kPa/(K·mol) In calculation, the units of R must match those for P,V,T and n.

PV = nRT nRT V = P 1.37 mol x 0.0821 x 273.15 K V = 1 atm V = 30.6 L What is the volume (in liters) occupied by 49.8 g of HCl at STP? T = 0 0C = 273.15 K P = 1 atm PV = nRT n = 49.8 g x 1 mol HCl 36.45 g HCl = 1.37 mol V = nRT P V = 1 atm 1.37 mol x 0.0821 x 273.15 K L•atm mol•K V = 30.6 L

P1V1 n1T1 R= P2V2 n2T2 R= P2V2 n2T2 P1V1 n1T1 = P2V2 T2 P1V1 T1 = As for the other laws, the ideal gas law can be rewritten as: and rearranged to find the new value of one of the variables when the other three change simultaneously. For instance: V2 = V1 * (P1/P2) * (n2/n1) * (T2/T1) P1V1 n1T1 R= P2V2 n2T2 R= P2V2 n2T2 P1V1 n1T1 = P2V2 T2 P1V1 T1 = If n1=n2

Boyle’s Law and Gay-Lussac’s Law can be combined to form a single, slightly more complicated law: P*V/T = constant or P1V1/T1 = P2V2/T2 This relationship is called the combined gas law.

The combined gas law may be used to calculate the change in one of the three variables when the other two variables both change at the same time. P2V2/T2 = P1V1/T1 What is the new pressure of a gas when the temperature and volume are both simultaneously changed? P2 = P1 * (V1/V2) * (T2/T1) What is the new temperature of a gas when both the pressure and the volume are simultaneously changed? T2 = T1 * (P2/P1) * (V1/V2) What is the new volume of a gas when both the temperature and the pressure are simultaneously changed? V2 = V1 * (P1/P2) * (T2/T1)

PV = nRT n, V and R are constant nR V = P T = constant P1 T1 P2 T2 = 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)? PV = nRT n, V and R are constant nR V = P T = constant P1 = 1.20 atm T1 = 291 K P2 = ? T2 = 358 K P1 T1 P2 T2 = P2 = P1 x T2 T1 = 1.20 atm x 358 K 291 K = 1.48 atm

If the value of n in the ideal gas equation (PV = nRT) is interpreted as g/M, where g is the mass in grams of the gas and M is the molar mass of the gas in grams/mole, we can write a new equation: which can be rearranged to:

These two equations are both very useful. The first equation allows the molar mass of gas molecules to be determined by weighting a sample of gas at a known temperature, pressure, and volume. The second equation allow the determination of the molar mass if the density (d = g/V) of the gas is known. It also allow the density of a gas to be determined if its molar mass is known.

d is the density of the gas in g/L Density (d) Calculations m is the mass of the gas in g m V = PM RT d = M is the molar mass of the gas Molar Mass (M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L

When two different gases are mixed together, their behavior is described by Dalton’s law of partial pressures. The total pressure exerted by both gases is simply the sum of the individual pressures (partial pressures) that each would exert if the other were not there. Ptotal = PA + PB In words this might be stated that a mixture of 1 mole of O2 and 2 moles of N2 in a volume of 1 liter would have the same total pressure as 2 moles of O2 and 1 mole of N2 or as 3 moles of He.

When gases are collected over water, some of the gas collected is water vapor. The vapor pressure of water is determined by the temperature and can be looked up in a table. If the atmospheric pressure were 755 torr, and the vapor pressure of water were 23.0 torr then: Patmosphere = Pgas + Pwater 755 torr = pgas + 23.0 torr Pgas = 732 torr

V and T are constant P1 P2 Ptotal = P1 + P2 Dalton’s Law of Partial Pressures Partial pressure is the pressure of the individual gas in the mixture. V and T are constant P1 P2 Ptotal = P1 + P2 5.6

PA = nART V PB = nBRT V XA = nA nA + nB XB = nB nA + nB PT = PA + PB Consider a case in which two gases, A and B, are in a container of volume V. PA = nART V nA is the number of moles of A PB = nBRT V nB is the number of moles of B XA = nA nA + nB XB = nB nA + nB PT = PA + PB PA = XA PT PB = XB PT Pi = Xi PT mole fraction (Xi) = ni nT 5.6

Group practice problem chap4-5:Q21 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)? Pi = Xi PT PT = 1.37 atm 0.116 8.24 + 0.421 + 0.116 Xpropane = = 0.0132 Ppropane = 0.0132 x 1.37 atm = 0.0181 atm Group practice problem chap4-5:Q21 5.6

General Rule: The greater a gas’s partial pressure in a gas mixture, the greater the extent to which that gas will dissolve in any liquid present. This relationship is described by Henry’s law.

Henry’s law for a pure gas: Henry’s law for a mixture of gases: CH is known as the Henry’s law constant. It has a unique value for each particular gas and each temperature.

Because the amount of gas dissolved in a liquid at a given temperature depends only upon the partial pressure of the gas, this value is often reported as the gas solubility. The solubility of gas reported in units of pressure is referred to as the gas tension. Because the concentration of N2 in the blood is not affected by an person’s metabolism, the blood is saturated with N2 at all times. The pressure exerted on a diver increases by 1 atm for every 10 m of depth of water. This results in significant quantities of N2 dissolving in the blood due to breathing air at a high pressure. If the diver returns to the surface too quickly, pressure of the air being breathed is much less and the dissolved N2 gas forms bubbles in the blood causing a disease called the bends (also called caisson disease).

The solubility of any gas decreases as the temperature increases. This behavior accounts for the loss of dissolved CO2 in carbonated beverages as they warm up.

Chapter 5 Summary Properties of Gases • The physical properties of all gases depend on only four variables: pressure (P), volume (V ), temperature (T ), and number of moles (n).

Quantitative Description of Gas Behavior Chapter 5 Summary Quantitative Description of Gas Behavior • Boyle’s law is a mathematical description of the relation between gas pressure and volume when the temperature and number of moles of gas remain constant. • Charles’s law is a mathematical description of the relation between gas volume and temperature when the gas’s pressure and the number of moles of gas remain constant. • Gay-Lussac’s law is a mathematical description of the relation between gas temperature and pressure when the gas’s volume and number of moles remain constant. • Avogadro’s law is a mathematical description of the relation between gas volume and number of moles when the gas’s temperature and pressure remain constant.

Chapter 5 Summary The Combined Gas Law • Three of the gas laws (Boyle’s, Charles’s, and Guy-Lussac’s) can be combined to predict results when two variables are changed simultaneously.

Chapter 5 Summary The Ideal Gas Law • All four gas variables, P, V, T, and n, can be combined into the ideal gas law. It is used to predict the behavior of gases when mass is a consideration and to determine the molar mass of gaseous substances.

Chapter 5 Summary Mixtures of Gases • The pressures of different gases in a mixture are called partial pressures. Dalton’s law of partial pressures states that the total pressure of a gas mixture is equal to the sum of the partial pressures.

Chapter 5 Summary Gases in Liquids • The amount of a gas that will dissolve in a liquid depends chiefly on the gas pressure and is described by Henry’s law. As the gas pressure increases, more gas will dissolve.