Charles’, Boyle’s, and Dalton’s LAWS Mahek and Kenny Present A Hall Production

Gases … What Are They Like? Gases are composed of widely separated particles in constant, random motion. Gases flow readily and occupy the entire volume of their container. Vapor – a gas that is a liquid at room temperature and pressure (water vapor and methanol vapor, but gaseous oxygen and gaseous hydrogen). Many low molar mass molecular compounds are either gases or easily vaporizable liquids.

An Introduction to Kinetic-Molecular Theory Provides a model for gases at the microscopic level. Pressure: collision of gas molecules with wall of container. Temperature: related to average speed of gas molecules. Molecules are in rapid, random motion. Movement of gases through three-dimensional space is called translational motion.

Pressure is the amount of force applied to an area. Pressure Atmospheric pressure is the weight of air per unit of area. P = FAFA

Units of Pressure Pascals –1 Pa = 1 N/m 2 Bar –1 bar = 10 5 Pa = 100 kPa

Units of Pressure 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

Barometers Used to measure atmospheric pressure. One atmosphere (atm): pressure exerted by a column of mercury exactly 760 mm high. One millimeter of mercury is called a Torr. 1 atm= 760 mmHg = 760 Torr = kPa

Boyle’s Law: Pressure-Volume Relationship For a fixed amount of a gas at constant temperature, the volume of the gas varies inversely with its pressure. For a fixed amount of a gas at constant temperature, the product of pressure and volume is a constant. PV = constant or P initial V initial = P final V final

Graphical Representation of Boyle’s Law When volume is increased there is more area for the molecules to “hit”; less force per area. Estimate the pressure at 3V and at 5V. Which plot is easier to use for making this estimation?

Charles’s Law: Temperature-Volume Relationship The volume of a fixed amount of a gas at constant pressure is directly proportional to its Kelvin (absolute) temperature. Absolute zero is the temperature obtained by extrapolation to zero volume. Absolute zero on the Kelvin scale = – °C

Graphical Representation of Charles’s Law When temperature is decreased (constant P) … … volume decreases. Extrapolation to the lowest possible volume (zero) gives the lowest possible temperature (0 K).

The Combined Gas Law We can cancel any term (P, V, n, T) that is the same on both sides. a V = —— P V = bTV = cn nT Therefore V α —— P PV and —— = a constant OR nT P 1 V 1 P 2 V 2 —— = —— n 1 T 1 n 2 T 2

The Ideal Gas Law P in atm, V in L, n in moles, T in kelvins. If any other units are used for these variables, a different value for R must be used … R = (L·atm)/(mol·K) The ideal gas constant  The ideal gas law PV = nRT PV —— = constant = R nT

Mixtures of Gases: Dalton’s Law of Partial Pressures Dalton’s law of partial pressures is used in dealing with mixtures of gases. The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the separate gases: P total = P 1 + P 2 + P 3 + … Partial pressure: the pressure a gas would exert if it were alone in the container. n 1 RT P 1 = ——— V n 2 RT P 2 = ——— V n 3 RT P 3 = ——— … V

Partial Pressures Illustrated Partial pressure of H 2 is 2.9 atm. Partial pressure of He is 7.2 atm. What would be the total pressure if 0.90 mol of N 2 were added to the gas mixture in (c)? Hmm … partial pressure appears to be related to the number of moles of gas …

Mole Fraction Since pressure (at constant T and V) is directly proportional to number of moles: We can find the partial pressure of a gas from its mole fraction and the total pressure. n 1 x 1 = —— n total The mole fraction (x) of a gas is the fraction of all the molecules in a mixture that are of a given type. P 1 x 1 = —— P total or P 1 = x 1 P total

Collection of Gases over Water As (essentially insoluble) gas is bubbled into the container for collection, the water is displaced. The gas collected is usually saturated with water vapor. … what TWO gases are present here? Assuming the gas is saturated with water vapor, the partial pressure of the water vapor is the vapor pressure of the water. P gas = P total – P H 2 O(g) = P bar – P H 2 O(g) If O 2 is being generated …

Practical Applications Hot air balloons are a good illustration of Charles' law because gases expand when they're heated. A bicycle pump illustrates Boyle's law: if you put your finger over the end of a bike pump and push in the plunger, the gas pressure inside will increase, and you'll feel it trying to push your finger out of the way. A practical application of Dalton’s law would be to take gasses that are collected over water in a laboratory, these gas during collection it become water vapor and moist.