Gases

Parameters to describe gases: Pressure Temperature number of molecules Volume

Pressure force = m x a = kg x m/s2 = Newton area (N) Barometer – a device used to measure atmospheric pressure. Evangelista Torricelli (early 1600s) used mercury for the first type of barometer

Units of pressure 760 mm Hg = 760 torr = 1 atmosphere (atm) = 101.3 kPa (kilopascals) = 14.7 psi The SI unit for pressure is named after Blaise Pascal. A Pascal is defined as 1 Newton acting on an area of one square meter. 1 N/m2

Relationship between Pressure, Force, and Area Force = mass x acceleration (On Earth acceleration is a constant due to gravity) Force = 500 N Force = 500 N Area of contact = 325 cm2 Pressure = force area = 500 N = 1.5 N/cm2 325 cm2 Area of contact = 13 cm2 Pressure = force area = 500 N = 38.5 N/cm2 13cm2 Area of contact = 6.5 cm2 Pressure = force area = 500 N = 77 N/cm2 6.5 cm2

STP Kelvin = °C + 273 Standard temperature and pressure are defined as 1 atm of pressure and 0C. When describing gases Kelvin temperature is typically used. Kelvin = °C + 273

Graham’s Law http://image.tutorvista.com/content/matter-states/diffusion-effusion-process.gif

NH3 + HCl  NH4Cl http://www.docbrown.info/page03/3_52states/NH3HCldiffexpt.gif

Graham’s law of Effusion The rates of effusion of gases at the same T and P are inversely proportional to the square roots of their molar masses.

Derivation of Graham’s Law Comparing two gases, “A” and “B.” At the same T their KE is equal. KEA = KEB ½ MAvA2 = ½ MBvB2 Multiplying both sides by 2 and rearranging to compare velocities gives: vA2 = MB vB2 MA

𝑉𝐴 𝑉𝐵 = 𝑀𝐵 𝑀𝐴 Now, take the square root of both sides: This shows that 𝑉𝐴 𝑉𝐵 = 𝑀𝐵 𝑀𝐴 This shows that 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑨 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑩 = 𝑀𝐵 𝑀𝐴 This can also be used when dealing with densities of gases. 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑨 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒆𝒇𝒇𝒖𝒔𝒊𝒐𝒏 𝒐𝒇 𝑩 = 𝑀𝐵 𝑀𝐴 = 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝐵 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝐴

Dalton’s Law of partial pressures The total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases. PT = P1 + P2 + P3 + . . . . . . . http://www.mayoclinic.org/tradition-heritage artifacts/images/2-1-med.jpg

Collecting gases over water Many gases are collected over water, thus according to Dalton’s law of partial pressures you must account for the vapor pressure of the water. Patm = Pgas + PH2O A table of water vapor pressures will be provided for you. http://www.mayoclinic.org/tradition-heritage-artifacts/images/2-1-med.jpg

P1V1 = P2V2 PV = k Boyle’s Law - 1662 pressure-volume relationship: the volume of a fixed mass of gas varies inversely with the pressure at constant temperature PV = k P1V1 = P2V2 http://scienceworld.wolfram.com/biography/pics/Boyle.jpg

Boyle’s Law graph http://chemwiki.ucdavis.edu/@api/deki/files/2839/=BoylesLaw.jpg

Charles’s Law - 1787 V = k V1 = V2 T T1 T2 (Kelvin temp) volume-temperature relationship: volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature.) His experiments showed that all gases expand to the same extent when heated through the same temperature interval. Charles found that the volume changes by 1/273 of the original volume for each Celsius degree, at constant pressure and an initial temperature of 0C. V = k V1 = V2 T T1 T2 (Kelvin temp)

Charles’s Law graph http://image.tutorvista.com/content/matter-states/volume-temperature-variation.gif

Gay-Lussac’s Law - 1802 pressure-temperature relationship: The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature. For every Kelvin of temperature change, the pressure of a confined gas changes by 1/273 of the pressure at 0C. P = k P1 = P2 (Kelvin temp) T T1 T2

Gay-Lussac graph http://images.brighthub.com/92/2/9223BD5E09B41611EDADC008DC5BDB61313227FC_small.jpg

T T1 T2 Combined gas law pressure, volume and temperature relationship   PV = k P1V1 = P2V2 T T1 T2 (Kelvin temp)

Gay-Lussac’s Law of Combining Volumes - 1808 at a constant T and P, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers.

standard molar volume of gas Avogadro’s Law equal volumes of gases at the same T and P contain the same number of molecules.   The volume occupied by one mole of a gas at STP is known as standard molar volume of gas 22.4 liters.

Ideal Gas Law The Ideal Gas Law is the mathematical relationship among pressure, volume, temperature, and the number of moles of a gas. Combining Boyle’s Law, Charles’s Law and Avogadro’s Law gives us V = nRT or more P commonly seen as PV = nRT

R – the ideal gas law constant R = PV = (1 atm)(22.4 l) = 0.082 l·atm nT (1 mol)(273.15K) mol·K Other values for R (depending on P units) 62.4 l·torr (or mm Hg) 8.314 l ·kPa mol ·K mol· K

Variations on the ideal gas law Variations on the ideal gas law can be used to find Molar mass or density. (n [moles] = m/M) PV = mRT or M = mRT m= mass M PV M = molar mass Density is m/V so substituting that into the ideal gas equation gives us M = mRT = DRT which then gives us D = MP PV P RT

Deviations of real gases from ideal behavior The molecules of an ideal gas are assumed to occupy no space and have no attractions for each other. Real molecules, however, do have finite volumes, and they do attract one another. In 1873, Johannes van der Waals accounted for this behavior by devising a new equation (based on the ideal gas law) to describe these deviations  

Van der Waals equation P = nRT - n2a V-nb V2   Correction for Correction for volume of molecules molecular attractions   The volume is decreased by the factor nb, which accounts for the finite volume occupied by gas molecules. The pressure is decreased by the second term, which accounts for the attractive forces between gas molecules. The magnitude of a reflects how strongly the gas molecules attract each other. The more polar the molecules of a gas are, the more they will attract each other. At very high pressures and very low temperatures deviations from ideal behavior may be considerable.