Gas Laws Notes PDF - Molar Mass, Density & Calculations
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Oklahoma State University
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This document provides notes and practice problems on gas laws, focusing on molar mass, density, and related calculations. It covers concepts such as the Ideal Gas Law, Dalton's Law of Partial Pressures, and Graham's Law, offering worked examples and practice questions to reinforce understanding of these key chemistry principles.
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Name: More Gas Laws Notes: Additional Notes: Molar Mass and Density You can rearrange the IDEAL gas law in order to solve for density or molar mass of a gas. P = Pressure...
Name: More Gas Laws Notes: Additional Notes: Molar Mass and Density You can rearrange the IDEAL gas law in order to solve for density or molar mass of a gas. P = Pressure V = volume The Ideal gas law is: n = moles PV = nRT T = temperature (Kelvin only) We know that density is mass divided by volume. R = Universal Gas Constant π m = mass d= π β³ = Molar mass d = density We know that the molar mass is mass divided by the number of moles. β³= π π If you do a little rearranging of the molar mass formula above you can solve for moles. π n= β³ π Replace moles in the Ideal gas law with ( ) into the ideal gas law: β³ π ππ π ππ = ( β³ ) π π or ππ = β³ You can rearrange this to solve for the molar mass. ππ π β³ = ππ You can also rearrange this to solve for the density. π π π ππ π β³π β³ = π π or β³ = π β π= π π What is the density of carbon monoxide, CO, at 298 K and 1.5 atm? A Chemistry Guide Daltonsβ Law of Partial Pressures The pressure of a mixture of gases is equal to the sum of the pressures of all of the individual gases. PTot = PA + PB + PC +β¦+P... Remember that the mole fraction, Ο, can be calculated using the following formula: π π ΟA = π΄ ππ‘ππ‘ππ and ΟB = π΅ ππ‘ππ‘ππ etc. Then you can use the mole fraction and the total pressure to calculate the partial pressure for any gas in the system. PA = ΟA Ptotal and PB = ΟB Ptotal etc. Example: A mixture of oxygen, hydrogen and nitrogen gases exerts a total pressure of 278 kPa. If the partial pressures of the oxygen and the hydrogen are 112 kPa and 101 kPa respectively, what would be the partial pressure exerted by the nitrogen? Grahamβs Law of Effusion Graham's Law shows the relationship between the molar mass of a gas and the rate at which it will effuse. Effusion is the process of gas molecules escaping through tiny holes in their container. Diffusion can also be considered with Graham's Law, such as perfume diffusing through a room. The central concept is based on the fact that large particles travel slower than small particles when they escape through a hole in a container. π ππ‘π ππ πΈπππ’π πππ πππ πΊππ π΄ πππππ πππ π πΊππ π΅ π ππ‘π ππ πΈπππ’π πππ πππ πΊππ π΅ = πππππ πππ π πΊππ π΄ Example: What is the molecular weight of a gas which diffuses 1/50 as fast as hydrogen, H2,? (molar mass of hydrogen is 2.02 g/mol) A Chemistry Guide I do: Answer: A sample NaHCO3 was decomposed and the CO2 gas was collected by bubbling it through water. As the CO2 gas passes through the water, it picks up water vapor and is considered βwet.β The partial pressure of the water at 26.0Β°C is 25.2 torr. If the total pressure of the mixture of water vapor and carbon dioxide gas is 772.4 torr, what is the pressure of the βdryβ carbon dioxide gas? We do: At a certain temperature, hydrogen molecules move at an average velocity of 1840 m/s. Estimate the molar mass of a gas whose molecules have an average velocity of 311 m/s. A Chemistry Guide We do: An unlabeled gas cylinder containing 0.500 L of gas was found. The monatomic gas was analyzed at 15.0 Β°C and 0.968 atm. The sample weighed 2.688 grams. Calculate the molar mass of the gas and then use that to determine its identity. You do: 1) What is the density of N2O in g/L at 25.67 Β°C and 1.06 atm? (Molar Mass N2O = 44.02 g/mole) 2) A canister containing 4.50 mol of nitrogen, N2, and 2.07 mol of oxygen, O2, has a total pressure of 105.2 kPa. What is the partial pressure of the oxygen? 3) If H2 gas effused from a container at a rate of 10.0 mL every second, what would the rate of effusion for O2 gas in the same container at the same conditions? 4) If 3.13 g of Gas A occupies 1.12 L at 113 kPa and 45.0Β°C, what is the molar mass? A Chemistry Guide 5) A gas was collected over water in an eudiometer tube at 19.0 Β°C. The total pressure of the gases in the eudiometer tube was 772.2 mm Hg and the volume of the gas was 45.1 mL. The vapor pressure of water at 19.0 Β°C is 16.5 mm Hg. What was the pressure of the dry gas? 6) Consider the gas in question #5), what was the mass of the gas in the tube if it was NO? (Think moles first!) 7) A sample of natural gas contains 8.010 moles of CH4, 0.731 moles of C2H6 and 0.190 moles of C3H8. If the total pressure of the gas is 5.25 atm, what is the partial pressure of just the propane (C3H8)? A Chemistry Guide
