The Ideal Gas LawThe Ideal Gas Law Section 4.4 Pg

IDEAL GAS LAWIDEAL GAS LAW  Before getting too far into this law, it is important to understand the difference between an ideal gas and a real gas....  IDEAL GAS – does not really exist, it is hypothetical  Follows all gas laws perfectly under all conditions  Does not condense when cooled  Assumes that the particles have no volume and are not attracted to each other  REAL GAS – does not follow gas laws exactly, it deviates at low temperatures and high pressures  Condenses to liquid or sometimes solid when cooled or under pressure  Particles are attracted to each other and have volume  Behaves like an ideal gas at higher temperatures and lower pressures

Ideal vs. Real GasesIdeal vs. Real Gases (a)In an ideal gas, the molecules collide like perfectly hard spheres and rebound very quickly after collision. (b) In a real gas, the molecules are “soft” (can be deformed) and intermolecular attractions are important. The process of collision takes a slightly longer time, as a result.

We will be dealing with gases as if they were ideal In 1873, Johannes van der Waals hypothesized the existence of attractions between gas molecules to explain deviations from the ideal law. The general forces of attraction, called van der Walls forces, include dipole-dipole and London forces. Johannes van der Waals ( )

IDEAL GAS LAWIDEAL GAS LAW  Describes the interrelationship of pressure, temperature, volume and amount (moles) of matter; the four variables that define a gas system  REMEMBER:  Boyle’s Law: Volume is inversely proportional ( α) to pressure V α 1/P  Charles’ Law: Volume is directly proportional to temperature V α T  Avogadro’s Theory: Volume is directly proportional to chemical amount (mol) V α n  From all of these comparisons to volume: V α 1 x T x n= V α T n P P V = R T nR is a constant called the universal gas constant P(allows us to change from α to =) V = nRTPV = nRT (ideal gas law) P

 Notice which Variables are directly proportional and which ones are inversely proportional.  pressure and volume are on the same side of the equal sign and therefore are inversely proportional.  Pressure and temperature are on the opposite sides of the equal sign and therefore are directly proportional.

R = universal gas constantR = universal gas constant  Depends on STP or SATP, atm or kPa  Units: L kPa/mol Kvalue = L kPa/mol K  Units: L atm/mol Kvalue = L atm/mol K Make sure you look at the unit for pressure to decide which R value to use  Any idea how we came up with the number??  You substitute SATP or STP conditions for one mole into the ideal gas law and solve for R R = PV= ( kPa)(22.414L) = L kPa/mol K. nT (1.0 mol)(273.15K)

Using the Ideal Gas LawUsing the Ideal Gas Law  When solving for the ideal gas law, start by listing your variables. If three are known of the four, you can solve for the last one. Example One: What mass of neon gas should be introduced into an evacuated 0.88L tube to produce a pressure of 90 kPa at 30°C? P = 90 kPa V = 0.88L T = 30°C  303K R = L kPa/mol K m = ? n = ? PV = nRT n = PV RT n = (90kPa)(0.88L) (8.314 LkPa/molK)(303K) n = mol x g = 0.63 g 1 mol

Using the Ideal Gas Law – PracticeUsing the Ideal Gas Law – Practice 2. A rigid steel cylinder with a volume of 2.00 L is filled with nitrogen gas to a final pressure of 20.0 atm at 27°C. How many moles of N2 gas does the cylinder contain? P = 20.0 atm PV = nRT V = 2.00 L n = PV/RT T = 27 °C = 300 Kn = (20.0 atm)(2.00L) R = Latm/molK ( Latm/molK) (300K) n = ? n = mol n = 1.62 mol

Using the Ideal Gas Law – PracticeUsing the Ideal Gas Law – Practice 3. Predict the volume occupied by 0.78 g of hydrogen at 22°C and 125 kPa P = 125 kPa V = ? T = 22 °C = 295 K R = LkPa/molK m = 0.78g n = ? n H2 = 0.78 g x 1 mol = mol 2.02g PV = nRT  V = nRT P V = (0.386 mol)(8.314LkPa/molK)(295K) 125 kPa V = L V = 7.6 L

Homework  Pg. 174 #3-5  Pg.176 # 1,2,6,9,11