GAS LAWS & KINETIC THEORY OF GASES Jeff Natcher

GAS LAWS BOYLE’S LAW Boyle’s law describes the relationship between P and V of a gas. P=(nRT) 1/V, where nRT is a constant P is inversely proportional to V As a formula: P1/P2=V2/V1 (only for constant temp.) P1=Original PressureP2=New pressure V1=Original VolumeV2=New Volume History: First stated by Robert Boyle in ♣♣

BOYLE’S LAW PROBLEMS Side note: SI Units for pressure are: Pascal (Pa) and N/m^2 SI Units for Volume are: m^3 A balloon is inside a vacuum. The balloon has a volume of.63 m^3. The pressure inside the balloon is 1.2 Pa. The vacuum forces air out of the chamber and doubles the volume of the balloon. What is the new pressure of the air inside of the balloon? The volume doubles, so the pressure is halved:.63 * 2 = 1.26 m^3 (V2) 1.2 * 0.5 = 0.6 Pa (P2)

GAS LAWS CHARLES’ LAW Charles’ Law describes the relationship between V and T of a gas, and P and T of a gas. V= (nR/P) T, where (nR/P) is a constant All gases expand equally for the same rise of temperature if they are held at constant pressure. P= (nR/V) T, where (nR/V) is a constant The pressures of all gases increase equally for the same rise of temperature if they are held at constant volume. History: Named after Jacques A.C. Charles, a French physicist who originally formulated it. ♣♣

CHARLES’ LAW PROBLEMS Side note: SI unit for volume is m^3 SI unit for pressure is Pa or N/m^2 Unit for temperature is mostly °K A hot air balloon is filled with air that is 90°K. The air inside has a pressure of 1 N/m^2. Assuming that no air escapes the balloon, what would the temperature of the air be if the pressure increased to 1.3 N/m^2? The pressure increased by a factor of 1.3, and the volume remained the same, so the temperature must also increase by a factor of * 1.3 = 117°K.

GAS LAWS AVOGADRO’S LAW Avogadro’s Law describes the relationship between the volume and the number of moles of atoms of the particular gas in a given situation. V/n = k The volume the gas takes up is proportional to the number of moles of the substance there are, assuming the pressure and temperature remain the same. k is a constant History: Amedeo Avogadro was an Italian physicist and lawyer. Published 2 memoirs: one in 1811, one in The law was stated separately by Ampere in Avogadro and Ampere are generally interchangeable in terms of history.

AVOGADRO’S LAW PROBLEMS A jar full of 1 mL of evaporated water contains k moles of the compound H2O. Half of the volume of gas is expelled from the jar, leaving how many moles of the compound H2O still in the jar (in terms of k). k mol takes up the volume of the inside of the jar. So ½ the amount of vapor in the jar means there are ½ the amount of moles of the substance. So the number of moles must be (1/2)k.

GAS LAWS IDEAL GAS LAW Ideal gas law relates T, V, & P in terms of each other so anyone can calculate any of these three if given two of them. PV=nRT P=(nRT)/V History: First stated by Emile Clapeyron in Basically a combination of Charles’ and Boyle’s law.

IDEAL GAS LAW PROBLEMS Assuming n and R remain constant: The pressure of a gas in a container is 14 Pa. The volume of the container is 4 m^3. What is the temperature of the gas in the container? 14 Pa * 4 m^3 = 56° What is the Volume of a fluid with a temperature of 76° and a pressure of 36 Pa? 76° / 36 Pa = 2.11 m^3

KINETIC THEORY OF GASES Kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container they are held in. Basically, everything is always in motion; there is never a still moment.

REAL WORLD APPLICATION A simple way to connect all of these laws to real life is to think of a balloon. Why a balloon? Because it is a flexible container of gas that demonstrates all the laws in different ways easily. A balloon in a vacuum: Pressure decreasing outside the balloon makes the balloon expand because it has to maintain equilibrium with the gas outside the balloon, so the volume increases to make this possible. A balloon in a freezer: The volume of gas inside a balloon has a certain temperature. If the temperature outside the balloon decreases, the gas inside the balloon has to maintain equilibrium with the gas outside, so the particles inside slow down and get closer together to decrease the volume and the temperature.