Gases Foothill Chemistry

Pressure Force per unit area on a surface. Force is measured in Newtons (N). The force that will increase the speed of a 1 kg object one meter per second each second that the force is applied. 1 N = 1 kg  m/s2 (mass times acceleration) 1 atm = 10.1 N / cm2 1 Pa = 1 N / m2

Standard Temperature and Pressure Standard Temperature and Pressure (STP) have been agreed by scientists to be 1 atm of pressure and 0oC. 1 atm = 760 torr = 760 mm Hg = 101.325 kPa

Dalton’s Law of Partial Pressures The pressure of each gas in a mixture is call the partial pressure of that gas. The total pressure of a gas mixture is the sum of the partial pressures of its components. PT = P1 + P2 + P3 ... PT is the total pressure of the mixture and P1, P2, and P3 etc. are the partial pressures of the component gases.

Collection of Gas Over Water When collecting gas over water, there is some water vapor in the collected gas that makes the total gas pressure impure (there’s water vapor too). The partial pressure of water vapor must be subtracted from the total pressure to obtain an accurate (more accurate) measurement of the gas pressure collected.

Collection of Gas over Water

Water Vapor Pressure Correction Patm = Pdesired gas + Pwater vapor Patm – read from the laboratory barometer Pwater vapor (PH2O)– comes from a standard water vapor pressure table Temp oC Pressure (mm Hg) Pressure (kPa) 0.0 4.6 0.61 30 31.8 4.25 5.0 6.5 0.87 50 92.5 12.34 20.0 17.5 2.34 70 233.7 31.18 25.0 23.8 3.17 100 760.0 101.33

Expanded Water Vapor Pressure Table

Nature of Gases Expansion – Gases do not have definite shape, they fill any container in which they are enclosed. Fluidity – Attractive forces between particles are insignificant so they glide past each other. Gases flow – they are considered fluids. Low Density – Particles are relatively far apart. Compressibility - Gases can be crowded closer together using pressure. Diffusion and Effusion Diffusion – Spontaneous mixing caused by random motion (spreading out) Effusion – Process by which gas particles pass through a tiny opening

Effusion and Diffusion The rate of effusion and diffusion depend on the relative velocities (speed) of gas molecules. The velocity of a gas varies inversely with the square root of its molar mass. (Lighter molecules move faster than heavier molecules at the same temperature). ½ mAvA2 = ½ mBvB2 (Uh oh, here comes the math)

Graham’s Law of Effusion The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑜𝑓 𝐴 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑜𝑓 𝐵 = 𝑀𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝐵(𝑀𝐵) 𝑀𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝐴 (𝑀𝐴)

Sample Effusion Problem What is the ratio of the effusion rates of hydrogen to oxygen? 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑜𝑓 𝐻2 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑜𝑓 𝑂2 = 32.00 𝑔/𝑚𝑜𝑙 2.02𝑔/𝑚𝑜𝑙 ≈ 2 × 16 2 = 16 =4 or 4:1 ratio, where hydrogen’s effusion rate (velocity) is 4 times as fast as that of oxygen

Real Gases vs. Ideal Gases Real Gas – Does not behave completely according to the assumptions of the kinetic-molecular theory. High Pressure Low Temperature Attractive forces under these conditions do not allow for “ideal” behavior.

Gas Laws Boyle’s Law Charles’s Law Gay-Lussac’s Law Combined Gas Law Avogadro’s Law Ideal Gas Law

Boyle’s Law The volume of a fixed mass of gas varies inversely with the pressure at constant temperature 𝑃 1 × 𝑉 1 = 𝑃 2 × 𝑉 2 Pressure x Volume is a constant.

Charles’ Law The volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature 𝑉 1 𝑇 1 = 𝑉 2 𝑇 2

Gay-Lussac’s Law The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature. 𝑃 1 𝑇 1 = 𝑃 2 𝑇 2

Combined Gas Law Combining Boyle’s Law, Charles’ Law and Gay-Lussac’s Law into one mathematical expression 𝑃 1 × 𝑉 1 𝑇 1 = 𝑃 2 × 𝑉 2 𝑇 2

Avogadro’s Law Gay-Lussac’s Law – Combining Volumes of Gases - At constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. At the same temperature and pressure, balloons of equal volume have equal numbers of molecules, regardless of which gas they contain.

Finding Volume of an Unknown

Ideal Gas Law

Ideal Gas Constants