Chapter 5 Gases

Reactions Involving Gases in reactions of gases, the amount of a gas is often given as a volume the ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefficients in the equation as a mole ratio when gases are at STP, use 1 mol = 22.4 L P, V, T of Gas A mole A mole B P, V, T of Gas B

Examples How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP? O2(g) + 2 H2(g) → 2 H2O(g) What volume of O2 at 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO? 2 HgO(s)  2 Hg(l) + O2(g) The reaction used in the deployment of automobile airbags is the high- temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0 °C are produced by decomposition of 45.0 g NaN3? 2Na(s) + 3N2(g) 2NaN3(s)

Kinetic Molecular Theory the particles of the gas (either atoms or molecules) are constantly moving the attraction between particles is negligible when the moving particles hit another particle or the container, they do not stick; but they bounce off and continue moving in another direction like billiard balls there is a lot of empty space between the particles compared to the size of the particles the average kinetic energy of the particles is directly proportional to the Kelvin temperature as you raise the temperature of the gas, the average speed of the particles increases

Density & Pressure Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density result of the constant movement of the gas molecules and their collisions with the surfaces around them when more molecules are added, more molecules hit the container at any one instant, resulting in higher pressure also higher density

Gas Laws Explained – Dalton’s Law of Partial Pressures Dalton’s Law says that the total pressure of a mixture of gases is the sum of the partial pressures kinetic-molecular theory says that the gas molecules are negligibly small and don’t interact therefore the molecules behave independent of each other, each gas contributing its own collisions to the container with the same average kinetic energy since the average kinetic energy is the same, the total pressure of the collisions is the same

Dalton’s Law & Pressure since the gas molecules are not sticking together, each gas molecule contributes its own force to the total force on the side

Kinetic Energy and Molecular Velocities average kinetic energy of the gas molecules depends on the average mass and velocity KE = ½mv2 gases in the same container have the same temperature, the same average kinetic energy if they have different masses, the only way for them to have the same kinetic energy is to have different average velocities lighter particles will have a faster average velocity than more massive particles

Molecular Speed vs. Molar Mass in order to have the same average kinetic energy, heavier molecules must have a slower average speed

Temperature vs. Molecular Speed as the absolute temperature increases, the average velocity increases the distribution function “spreads out,” resulting in more molecules with faster speeds

Mean Free Path molecules in a gas travel in straight lines until they collide with another molecule or the container the average distance a molecule travels between collisions is called the mean free path mean free path decreases as the pressure increases

Diffusion and Effusion the process of a collection of molecules spreading out from high concentration to low concentration is called diffusion the process by which a collection of molecules escapes through a small hole into a vacuum is called effusion both the rates of diffusion and effusion of a gas are related to its rms average velocity

Graham’s Law of Effusion for gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of the molar mass for two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

Examples Determine how much faster Helium atoms moves, on average, than a carbon dioxide molecule at the same temperature Calculate the molar mass of a gas that effuses at a rate 0.462 times N2

Ideal vs. Real Gases Real gases often do not behave like ideal gases at high pressure or low temperature Ideal gas laws assume no attractions between gas molecules gas molecules do not take up space based on the kinetic-molecular theory at low temperatures and high pressures these assumptions are not valid

The Effect of Molecular Volume at high pressure, the amount of space occupied by the molecules is a significant amount of the total volume the molecular volume makes the real volume larger than the ideal gas law would predict van der Waals modified the ideal gas equation to account for the molecular volume b is called a van der Waals constant and is different for every gas because their molecules are different sizes

Real Gas Behavior because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures Tro, Chemistry: A Molecular Approach

The Effect of Intermolecular Attractions at low temperature, the attractions between the molecules is significant the intermolecular attractions makes the real pressure less than the ideal gas law would predict van der Waals modified the ideal gas equation to account for the intermolecular attractions a is called a van der Waals constant and is different for every gas because their molecules are different sizes

Real Gas Behavior because real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures

Van der Waals’ Equation combining the equations to account for molecular volume and intermolecular attractions we get the following equation used for real gases a and b are called van der Waal constants and are different for each gas

Real Gases a plot of PV/RT vs. P for 1 mole of a gas shows the difference between real and ideal gases it reveals a curve that shows the PV/RT ratio for a real gas is generally lower than ideality for “low” pressures – meaning the most important factor is the intermolecular attractions it reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideality for “high” pressures – meaning the most important factor is the molecular volume

Example A sample of 3.50 moles of NH3 gas occupies 5.20 L at 47oC. Calculate the pressure of the gas (in atm) using A) the ideal gas equation B) the van der Waals equation a = 4.17 atm •L/mol2 b = 0.0371 L/mol