Chapter 13: Gases Sec. 13.2: The Ideal Gas Law

Objectives zRelate the amount of gas present to its pressure, temperature, & volume by using the ideal gas law zCompare the properties of real & ideal gases

The Ideal Gas Law zIn previously covered gas laws, the principles held true for a “given amount” of gas or a “fixed mass” of gas. Why? zChanging the number of particles present will affect at least one other variable. yIf V & T are held constant, the number of particles will affect the P. yIf P & T are held constant, the number of particles will have an affect on the volume.

The Ideal Gas Law zWe can conclude P, V, T, and number of particles are interrelated. zSince the number of particles and moles are directly proportional, “n” (representing # of moles) can be used in a mathematical statement describing the relationship of the 4 variables listed above. zKeep in mind: n = moles = mass/molar mass.

The Ideal Gas Law PV = nRT zThe ideal gas law describes the physical behavior of an ideal gas in terms of P, V, T, and n of gas present. zR is called the ideal gas constant. Its exact value will depend on the units used for pressure.

R values z L-atm mol-K z8.314 L-kPa mol-K z62.4 L-mmHg mol-K zYou WILL be given the R value with a problem BUT it may not have the correct units. You may have to convert it.

For example If the R value you are given is L-atm but pressure is given in kPa, mol-K you can convert to kPa by multiplying: L-atm x kPa = L-kPa mol-K 1 atm mol-K

Practice Problems Use R values previously given. zCalculate the number of moles of gas contained in a 3.0 L vessel at 3000 K with a pressure of 1.50 atm. zDetermine the Celsius temperature of 2.49 moles of gas contained in a 1.00 L vessel at a pressure of 143 kPa. zCalculate the volume that a mol sample of a gas will occupy at 265 K and a pressure of atm.

Applying the Ideal Gas Law zThe ideal gas law can be used to calculate the molar mass and density of a gas if the mass of the gas is known. zRemember, the number of moles of a gas (n) is equal to the mass (m) divided by the molar mass (M) or n = m/M zPV = nRT becomes PV = mRT; M = mRT M PV

Rearrange... zM = mRT PV zRecall that density (D) = m/V zM = DRT P zD = MP RT

Practice Problems zHow many grams of gas are present in a sample that has a molar mass of 70 g/mol and occupies a 2.00 L container at 117 kPa and C? zWhat is the molar mass of a pure gas that has a density of 1.40 g/L at STP? zWhat is the density of a gas at STP that has a molar mass of 44.0 g/mol?

Real vs. Ideal Gases zAn ideal gas is one whose particles take up no space, are in constant random motion, have no intermolecular attractive or repulsive forces, and have perfectly elastic collisions. zNo gas is truly ideal. yAll gas particles have some volume. yAll gas particles have some intermolecular attractions. ySome energy is generally lost in collisions.

Real vs. Ideal Gases zAn ideal gas follows the gas laws under all conditions of T & P. zMost gases behave like ideal gases at most T & P levels. yIf the P is extremely high, however, the particles are forced so close together that the gas will liquefy. yIf the T is extremely low, the particles have slowed down so much that forces between molecules are felt & condensation occurs.

Real vs. Ideal Gases zIn addition, gases made up of polar molecules do not behave as ideal gases. The oppositely charged ends of polar molecules have large electrostatic forces. zAlso, larger gas molecules behave less like ideal gases that smaller ones do. The particles of gases made up of large molecules, like C 4 H 10, occupy more actual volume than particles of smaller molecules, like He.