# Gas Laws - PC\|MAC

Gas Laws KMT Recap 1. Particles are far apart relative to size. 2. All collisions are elastic. 3. Particles are in constant motion. 4. No forces of attraction between particles. 5. KE = 1/2mv2

Pressure Pressurethe force per unit area on a surface Increased with increased number of collision of molecules Depends on volume, temperature, and the number of molecules Units (standard pressure = 1.00 atm = 760. mm Hg = 101.3 kPa = 1.00 bar) 1 Pa

1 psi 1 Bar 1 Tor 1 atm Pascal = 1 N/m2 (SI unit) = 1 lb/in2 (English unit) = 6,891 Pa = 105 N/m2 = 101.3 kPa

= 1 mm Hg = 101.3 kPa = 760 mm Hg = 14.70 psi Measuring Pressure Barometerdevice used to measure atmospheric pressure Exact height of mercury depends on atmospheric pressure, or force per unit area. Manometer - used to measure gas pressure in a closed container

(lab setting) Gas Laws 3 laws -Boyles Law -Charles Law -Gay-Lussacs Law *All depend on pressure (atm), temperature (K), volume (L), and quantity

(n = moles) Change one variable, it affects all three. ***Do not worry about memorizing names of laws, only care about relationships!! Warm up (in your notes) Convert the following units of pressure: 1.) 7.89 atm = ____________ mm Hg

2.) 204.5 kPa = ___________ atm 3.) 2.00 atm = _____________ mm Hg Boyles Law Pressure-Volume relationship Volume of a fixed mass of gas varies inversely with the pressure at constant temperature. Why? KMT Decreased volume = more collisions = more pressure

Practice A sample of oxygen gas has a volume of 150.0 mL when its pressure is 0.947 atm. What will the volume be if its pressure increases to 0.987 atm and the temperature remains constant? Charless Law Temperature-Volume relationship

Volume of a fixed mass of gas varies directly with the temperature at constant pressure. UnitsTemperature is always in Kelvin. Why?? *A sample of neon gas occupies a volume of 752 mL at 25oC. What volume will the gas occupy at 50oC if the pressure remains constant? Gay-Lussacs Law

Pressure-Temperature relationship Pressure of a fixed mass of gas at constant volume varies directly with the temperature. Why?? Practice The gas in a container is at a pressure of 3.00 atm at 25oC. Directions on the container warn not to keep it in a place where the container exceeds 52oC. At what pressure would the container be at 52oC?

Combined Gas Law Combines Boyles, Charles, and Gay-Lussacs laws to express relationship between pressure, volume, and temperature. A helium-filled balloon has a volume of 50.0 L at 25oC and 1.08 atm. What volume will it have at 0.855 atm and 10oC?

On a clean sheet of paper How hot will a 2.3 L balloon have to get to expand to a volume of 400. L? Assume that the initial temperature of the balloon is 25oC. Turn in when finished. Ideal Gas Law Relates pressure, temperature, volume, and number of molecules of a gas

For IDEAL gases onlyonly useful if all five assumptions of KMT are followed. Deviations from ideal gas behavior happen if there is: high pressure low temperature polarity larger molecules All cause attractive forces to take over.

PV = nRT P = Pressure V = Volume n = moles of a substance R = ideal gas constant T = temperature Ideal gas constant

Derived from standard temperature, pressure, volume, and moles. R = = = 0.0821 R = = = 8.314 Practice 1.) Calculate the number of moles of gas contained in a 3.00 L container at 27C and 1.50 atm.

2.) Calculate the pressure of a 5.0 L container with 5.43 g of H2 gas at 298 K. Finding molar mass of a gas If the moles of a gas (n) is equal to the mass (m) divided by the molar mass (MM) then we can derive the ideal gas law to read:

PV = n R T PV = mR T MM Practice What is the molar mass of a gas sample that has a mass of 1.574 g that occupies a volume of 8.3 L at a temperature of 127 and a and a

pressure of 155.30 kPa? Finding Density Derived from ideal gas law. MM = What is the molar mass of a pure gas that has a density of 1.40 g/L at STP?

Practice 1.) A mixture of nitrogen and neon gases contains equal moles of each gas and has a total mass of 10.0 g. What is the density of this gas mixture at 500 K and 15.0 atm? Assume ideal gas behavior. 2.) The vapor pressure of solid iodine at 30.0 C is 0.466 mm Hg. a. How many milligrams of iodine will sublime into a 1.00 L flask? b. If 2.00 mg of I2 are used, what will the final pressure be?

c. If 10.00 mg of I2 are used, what will the final pressure be? Daltons Law of Partial Pressure Partial pressurepressure of each gas in a mixture (each gas in a mixture exerts pressure independently of the other gases present). Daltons law of partial pressuresthe total pressure of a gas mixture is the sum of the partial pressures of the component gases.

PT = P1 + P2 + P3 + The partial pressure of a gas depends on the number of moles of gas, the size of the container, and the temperature of the mixture Practice A mixture of 6.00 g of oxygen and 9.00 g of methane is placed in a 15.0 L vessel at 0oC. What is the partial pressure of each gas? What is the total pressure in the vessel?

Partial Pressures and Mole Fractions Amounts of given gases can also be related to partial pressure through mole fraction. A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol % CO2, 18.0 mol % O2, and 80.5 mol% Ar. Calculate the partial pressure of O2 in the mixture if the total pressure of the

atmosphere is to be 745 torr. If this atmosphere is in a 121 L space at 295 K, how many moles of O2 are needed? P1 = X1Pt X1 = mole fraction Collecting gas over water Common way of experimentally measuring the volume of a gas.

Measures displacement of water to get volume. Assumes atmospheric pressure is equal to pressure inside burrette or test tube if water levels are equal. Use Daltons Law to account for vapor pressure of water (Table helps determine vapor pressure of water at particular temperatures). Practice A sample of KClO3 is partially decomposed, producing O2 gas

that is collected over water. The volume of gas collected is 0.250 L at 26C and 765 torr total pressure. (a) How many moles of O2 are collected? (b) When dry, what volume would the collected O2 gas occupy at the same temperature and pressure? Vapor pressure of water at 26oC is 25.2 torr. Temperaturewhat does it

measure? What is the exact relationship? (KE)avg = Root Mean Square Velocity KE of particles is dependent on two things. Velocity of particles is determined as an average

urms = urms = Desired units for urms are meters per second. R = 8.3145 J/mol K 1 J = 1 kg m2/s2 M = mass of 1 mol of gas particles in kilograms

Calculate the root mean square velocity for the atoms in a sample of helium gas at 25 oC. Maxwell-Boltzmann Distribution Grahams Law of Effusion Rates of effusion of gases at the same temperature and pressure are inversely proportional to the square root of their molar masses.

Avogadros Law States the equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. KMT assumes gas molecules have no effect on the overall volume of the gas. 1 mole of Xe occupies the same amount of space as 1 mole of He.

Molar volume - the volume occupied by one mole of a gas at STP Avogadro determined that one mole of any gas at STP will occupy 22.4 L How many particles of gas will occupy a volume of 6.23 L at STP? What volume will 0.437 mol of gas occupy at STP? Gas Stoichiometry Reactions of gasestreat the same way as reactions of liquids and

solids. Coefficients also represent the volumetric relationships in the rxn. Gas problems How many liters of HCl can be produced from 54.00 L of H2 reacting with excess Cl2? Combine with Ideal Gas Law

5.0 L of methane reacts completely at 1.5 atm and 298 K with oxygen gas to produce what mass of carbon dioxide (by-product is water)? More practice 1.) Zn reacts with hydrochloric acid to produce ZnCl2 and hydrogen gas. What mass of Zn would be needed to produce 0.500 L of hydrogen at STP? 2.) Dinitrogen pentoxide decomposes into oxygen gas and nitrogen dioxide. If 5.00 L reacts at

STP, what volume of nitrogen dioxide is produced when measured at 25C and 1.45 atm?

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