PV = nRT Ideal Gas Law Ideal Gases Avogadro’s Principle Ideal Gas Law Calculations PV = nRT Print 1-3, 5, 7, 9, 11-16

Ideal Gases Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory. Gases consist of tiny particles that are far apart relative to their size. Collisions between gas particles and between particles and the walls of the container are elastic collisions (no KE is lost)

Ideal Gases (continued) Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion There are no forces of attraction between gas particles The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

Real Gases Do Not Behave Ideally Real gases DO experience inter-molecular attractions Real gases DO have volume Real gases DO NOT have elastic collisions

Deviations from Ideal Behavior Likely to behave nearly ideally Gases at high temperature and low pressure Small non-polar gas molecules Likely not to behave ideally Gases at low temperature and high pressure Large, polar gas molecules

Avogadro's Principle Avogadro’s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

Avogadro's Principle Avogadro’s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. V1 = V2 n1 n2

Avogadro's Principle (cont.) The molar volume of a gas is the volume 1 mol occupies at 0.00°C and 1.00 atm of pressure (STP). At STP, 1 mol of gas occupies 22.4 L.

A. Ideal Gas Law Combined gas law to ideal gas law Since n is proportional to V and P, it can be incorporated into the combined gas law. Ideal gas constant R = 0.0821 L-atm/mol-K

PV = nRT A. Ideal Gas Law Ideal Gas Law V = (L) n = (mol) P = (atm) V = (L) n = (mol) R = gas constant T = (K) (0.0821 L-atm/mol-K)

B. Calculations PV = nRT A 5.00 L balloon of gas is at 0.855 atm and 25oC. How many moles of gas are in the balloon? A balloon shrinks when submerged in cold water

B. Calculations PV = nRT A 5.00 L balloon of gas is at 0.855 atm and 25oC. How many moles of gas are in the balloon? (0.855 atm)(5.00 L) A balloon shrinks when submerged in cold water = n (0.0821)(298 K) (0.855 atm)(5.00 L) (0.0821)(298 K) = n = 0.175 mol

Molar mass and The Ideal Gas Law

Molar mass and The Ideal Gas Law 1. A 2.00 L flask is filled with propane gas (C3H8) at a pressure of 1.00 atm and a temperature of -15.0C. What is the mass of propane in the flask? M = mRT PV 44.11 = m(0.0821)(258) (1.00)(2.00) (44.11)(1.00)(2.00) = m = 4.16 g (0.0821)(258)

Molar mass and The Ideal Gas Law 2. Determine the molar mass of an unknown gas that has a volume of 247.3 mL at a temperature of 100C, a pressure of 0.980 atm, and a mass of 0.424 g. M = mRT PV = (0.424g)(0.0821)(373 K) = 53.6 g/mol (0.980 atm)(0.2473 L)

Quick Quiz! 1) Find the volume of a gas if 2.95 mol has a pressure of 0.756 atm at a temperature of 52.0°C. A) 22.4 L B) 16.7 L C) 104 L D) 59.5 L 16