Properties, Measuring, Calculations, The Gas Laws Gases Properties, Measuring, Calculations, The Gas Laws

Characteristics of Gases Gases are fluids “Any substance that can flow” Gases have a MUCH lower densities than liquids and solids Enables them to “float” away Gas particles are much farther apart

Review What was density again? If gases are much less dense, do you think they will frequently run into each other or seldom come into contact?

Gases are highly compressable Gas particles can be smooshed together compressed Think of a syringe or a soda bottle Gases fill the container completely, spread out. Collisions of gas molecules are what causes pressure. The more collisions, the higher the pressure Gas molecules in the atm collide with Earth’s surface, creating atmospheric pressure.

Pressure Pressure is “force divided by area” You need to know the force and area over which the force is being exerted. SI units for force is the newton, N One newton is the force that gives an acceleration of 1 m/s2 to an object whose mass is 1 kg. The SI unit of pressure is the pascal, Pa The force one newton over an area of one square meter.

Table 1, Pressure Units Unit Abbreviation Equivalent of pascals Atmosphere atm 1 atm = 101,325 Pa Bar bar 1 bar = 100.025 Pa Millimeter of Hg mm Hg 1 mm Hg = 133.322 Pa Pascal Pa 1 Pounds per sq. in. psi 1 psi = 6.89286x103 Pa Torr torr 1 torr = 133.322 Pa One mmHg is also equal to 1 torr 1 atm = 760 torr = 760 mmHg

Standard Temperature and Pressure Standard Temperature and Pressure, STP 273.15 K (0ºC), 1 atm Makes it easier to work with gases when they are at constant temperatures and pressure.

Kinetic-Molecular Theory The KMT – a model that is used to predict gas behavior. States that gas molecules are in constant rapid, random motion. Spaces between are VERY large compared to the sizes of the gas particles Explains the fluidity and compressibility

Measureable properties Pressure = P = pressure exerted by the gas Temperature = T = temperature in Kelvins of the gas Volume = V = total volume occupied by the gas Number of moles = n = number of moles of gas

Molarity (M) = mol solute / L solution Number of moles We know how to calculate this when given the mass and the identity of the compound Converting using the molar mass (mol/g) No different for gases How about if we are given the concentration? Molarity is a measurement of “how much is in solution” Solute = what is being dissolved Solvent = what is doing the dissolving Solution = the entire mixture, both solute and solvent Molarity (M) = mol solute / L solution

Practice with Molarity We can determine the number of moles using the concentration and volume, then stick it into one of the following gas laws. Keep this in mind  Practice: How many moles are in 10 mL of a 3 M HCl soln? What is the concentration of 25 mL of H2SO4 when 0.089 moles were added?

PV (at any point) = k, so: P1V1 = P2V2 Boyle’s Law Robert Boyle found that as pressure of a gas increases in a closed container, the volume of the gas decreases. The product of the pressure and volume (PV) remain constant as long as temperature remains the same. The inverse relationship between pressure and volume became known as Boyle’s Law PV (at any point) = k, so: P1V1 = P2V2

Practice with Boyle’s LAw A sample of oxygen gas has a volume of 5.8 mL at a pressure of 0.947 atm. What will the volume of the gas be at a pressure of 1.000 atm if the temperature remains constant? A sample of gas in a syringe has a volume of 9.66 mL at a pressure of 64.4 kPa. The plunger is depressed until the pressure is 94.6 kPa. What is the new volume, assuming constant temp.?

V/T (at any point) = k, so: Charles’s Law Heating a gas makes it expand, cooling it makes it contract We can relate these two if the pressure remains constant This direct relationship between temperature and volume is known as Charles’s Law V/T (at any point) = k, so: (V1/T1) = (V2/T2)

Practice with Charles’s Law A balloon is inflated to 665 mL volume at 27ºC. It is immersed in a dry-ice bath at -78.5ºC. What is its volume, assuming the pressure remains constant?

Gay-Lussac’s Law Temperature-Pressure Relationships As you increase the pressure, the temperature increases. As the pressure decreases, the temperature decreases. This direct relationship between temperature and pressure is known as Gay-Lussac’s Law. **Pressure of a gas is proportional to its absolute temp** P/T = k (at any point), so: (P1/T1) = (P2/T2)

Practice with Temperature-Pressure Relationships An aerosol can containing gas at 101 kPa and 22ºC is heated to 55ºC. Calculate the pressure of the heated can.

The Combined Gas LAw We can set these equations equal to a common variable and then set them equal to one another By doing this, we can derive a COMBINED GAS LAW P1V1 = P2V2 T1 T2 This equation enables us to make calculations consisting of varying pressures, temperatures, and volume (holding nothing but the number of moles constant).

Practice with the Combined A soda bottle has a volume of 1.50 L at 25ºC at standard pressure (1.00 atm). The bottle is then taken to the bottom of the ocean to a temp of 1.00ºC and a pressure of 0.67 atm. What will the new volume of this bottle be?

Volume-molar relationships Avogadro!! States at the same temperature and pressure, balloons of the same volume with contain the SAME number of moles of gas, REGARDLESS of the gasses identity. H2, O2, CO2, it does not matter!! 1 mole of gas = 22.41 L. The mass of a gas at 0ºC and 1 atm (STP) is equal to the gas’s molecular (molar) mass V = kn, where k is the proportionality constant

Problems with these No gas perfectly obeys all four of these laws under all conditions These assumptions work well for most gases and most conditions One way to model a gas’s behavior is to assume that the gas is an ideal gas that perfectly follows these laws Does not condense to a liquid at low temps Does not have forces or attraction or repulsion between the particles And is composed of particles that have no volume

The ideal gas law P V = n R T P = Pressure V = Volume n = number of moles of gas R = Universal gas constant 8.314 L*kPa*mol-1*K-1 or 0.0821 L*atm*mol-1*K-1 T = Temperature of gas

Practice with the Ideal Gas Law How many moles of gas are in 22.41 Liters at 101.325 kPa and 0ºC?

Deviations from the Ideal Gas Law A real gas deviates from the ideal gas behavior at low temperature and high pressure The volume of the particles themselves is close to the total volume, so the actual volume will be higher than calculated. So, with regards to the Ideal Gas Law, low temperature and high pressure is BAD!! Condensation and particle attractions as they get closer Remember This!!!

Diffusion and Effusion Diffusion – the movement of particles from regions of higher density to regions of lower density. Odor of ammonia smelling up the room Involves an increase in entropy (measure of randomness) Effusion – the passage of a gas under pressure through a tiny opening Like out of a leaking tire

Gay-Lussac’s Law of Combining Volumes This law states that the volumes of gases involved in a chemical change can be represented by the ratio of small whole numbers ___ H + ___ Cl  ___ HCl This tells us our 7 diatomics ARE, in fact, diatomic

Dalton’s Law of Partial Pressures Dalton showed that in a mixture of gases, each gas exerts a certain pressure as if it were alone with no other gases mixed with it The pressure of each gas in a mixture is call the Partial Pressure This is known as Dalton’s Law of Partial Pressures  Total pressure = sum of the pressures of all the components within it Ptotal = PA + PB + PC + … + Pn

Practice The gauge pressure in a tire is 28 psi, which adds to atmospheric pressure of 14.0 psi. What is the internal tire pressure in kPa? A gas sample has a volume of 125 mL at 91.0 kPa. What will its volume be at 101 kPa?

Practice A gas at 65ºC occupies 4.22 L. At what Celsius temperature will the volume be 3.87 Liters, at the same pressure? A scientist warms 26 mL of gas at 0.0ºC until its volume is 32 mL. What is its new temperature in Kelvin?

Practice A sample of hydrogen exerts a pressure of 0.329 atm at 47ºC. What will the pressure be at 77ºC, assuming constant volume? A cylinder of gas at 55 kPa and 22ºC is heated until the pressure is 655 kPa. What is the new temperature??

Practice A balloon has a volume of 1.25 liters and a temperature of 20ºC. The pressure when filled was 1.05 atm. The balloon was released and allowed to float away, reaching 1.87 kilometers where the pressure is 0.667 atm and a temperature of -100 C, what would the new volume of the balloon be?

Practice How many moles of argon are there in 20.0 L, at 25ºC and 101 kPa? How many moles of air are in 1.00 L at -23ºC and 101 kPa? A weather balloon is inflated with 12.0 g of He at -23ºC and 100.0 kPa. What is its volume?

Practice An unknown gas effuses at a speed one- quarter of that of He. What is the molar mass of the unknown gas? It is either sulfur dioxide of sulfur trioxide. Which gas is it?

Practice A mixture of CO2, CO, H2, and N2 are floating around in a reagent bottle. The pressure of the system is 0.25 atm. The pressures of the gases are 0.002 atm, 0.058 atm, 0.084 atm, and unknown, respectively. Calculate the pressure of the N2 component.

Homework: Worksheet attached to your notes, front and back