Gases
1 atm is equivalent to how many mmHg? Torr? KiloPascal?
1 atm = 760 mmHg = 760 torr = 101.325 kPa
What are the five assumptions of the kinetic molecular theory of gases?
1) no intermolecular forces; 2) negligible volume; 3) all collisions are elastic; 4) all collisions are random; 5) average kinetic energy is temperature.
What 3 conditions must be met for an ideal gas?
1- No intermolecular forces 2- The volume occupied by molecules is negligible compared to the volume occupied by the gas. 3- All collisions are perfectly elastic
What is the Boltzmann constant?
1.38 x 10^-23 J/K This constant is the bridge between the macroscopic and microscopic behavior of gases (the behavior of the gas as a whole and the individual gas molecules).
At STP, how many liters does one mole of an ideal gas occupy?
22.4 L
Experimenters notice that the molar concentration of dissolved oxygen in an enclosed water tank has decreased to one-half its original value. In an attempt to counter this decrease, they quadruple the partial pressure of oxygen in the container. What is the final concentration of the gas?
2x [O2]i Twice initial concentration.
We have an airtight piston. There is 1 mol of an ideal gas contained within the vessel under the piston at pressure of 100 kPa. The piston rests at 10 cm from the base of the vessel. The pressure in the vessel increases to 200 kPa as force is applied to the piston. What would be the new resting position of the piston from the base of the vessel? Assume the temperature is held constant at 300 K throughout the experiment.
5 cm. According to Boyle's law, P1V1 = P2V2 If you double the pressure, you half the volume.
A gas with a higher molar mass will diffuse more ______ than a gas with a lower molar mass according to ______'s law.
A gas with a higher molar mass will effuse more slowly than a gas with a lower molar mass according to Graham's law.
Why do deviations in ideal gas laws increase as the temperature is lowered toward its boiling/condensation point?
As the average speed of gas molecules decrease with decreasing temperatures, intermolecular forces become more significant, resulting in a lower volume than predicted by ideal gas laws.
What deviations from the ideal gas law happen at moderately high pressures?
As the gas approaches its condensation pressure, intermolecular forces cause the gas to occupy less volume than an ideal gas.
What deviations in the ideal gas law occur at extremely low temperatures?
As the temperature approaches 0 Kelvins (where volume would be compressed to zero, which is impossible) the volume will be greater than predicted for an ideal gas.
At low temperatures, the kinetic energy of gas molecules is ______ because
At low temperatures, the kinetic energy of the particles is reduced, so collisions with other particles or the walls of the container are more likely to result in significant changes in kinetic energy.
How does a mercury barometer work?
Atmospheric pressure creates a downward force on the pool of mercury at the base of the barometer while the mercury in the column exerts an opposing force (its own weight) based on its density. When the external air exerts a higher force than the weight of the mercury in the column, the column rises.
Pressure
Force per unit area.
Gases deviate from ideal behavior at _______ pressures , ______ volumes, and ______ temperatures because
Gases deviate from ideal behavior at higher pressures and lower volumes and lower temperatures, because they all force molecules closer together. The closer they are, the more they can participate in intermolecular forces, which violates the definition of an ideal gas.
The behavior of which of these real gases will be reflected most closely with the ideal gas law? CH4, Ne, CO2, or He?
He, because the correction terms in the Van der Waal's equation adjust for attractive forces and size. Helium and Neon are both relatively nonreactive, but He is smaller
Which gas will exert a higher pressure under the same, non-ideal conditions: methane or chloromethane?
If a is increased while b remains negligible, the correction term gets larger, and the pressure drops to compensate. Therefore, methane will behave more ideally than chloromethane because a is smaller for methane. The real pressure of methane will thus be higher (closer to ideal).
In which of the following situations is it impossible to predict how the pressure will change for a gas sample? 1- The gas is cooled at a constant volume. 2- The gas is heated at a constant volume. 3- The gas is heated, and the volume is simultaneously increased. 4- The gas is cooled, and the volume is simultaneously increased.
If both changes have the same effect on pressure, then we can still predict which way it will change. This is the case in 4. Cooling the gas and increasing its volume both decrease pressure. Number 3, on the other hand, presents too vague a scenario for us to predict the change in pressure definitively. Heating the gas would amplify the pressure, while increasing the volume would decrease it. Without knowing the magnitude of each influence, it's impossible to say whether pressure will increase, decrease, or stay the same.
If methane and isobutane are placed in the same size container under the same conditions, which will exert the higher pressure (consider both as having negligible attractive forces)?
Isobutane is larger and will thus have a larger correction term for the size of the molecule, b. This makes the term V - nb smaller. The pressure or volume must rise to compensate. Because the two gases are in the same size container, isobutane must exert a higher pressure.
Temperature
Measure of the average kinetic energy of a system and its transfer.
Calculate the density of a gas
PV = (m/M) RT ==> PM = m/vRT ==> density = PM/RT
Ideal Gas Law
PV=nRT
We want to plot number of molecules versus speed for 2 gases. One of the gases is 1.0 L of helium, and the other is 1.0 L of bromine. How would those two plots compare at STP?
Particles with small masses travel faster than those with large masses, so the helium gas corresponds to curve B, which has a higher average speed. Because the gases are at the same temperature (273 K), they have the same average kinetic energy.
In what ways do ideal gases differ from real gases?
Real gas molecules have non-negligible volume and attractive forces. Real gases deviate from ideal gases at high pressure (low volume) and low temperature.
What are STP conditions?
STP (273 K and 1 atm) is used for gas law calculations.
How would high elevations affect O2 absorption in the lungs?
Since atmospheric pressure is lower, O2 absorption in the alveoli is lower..
According to Henry's law, what's the relationship between solubility and partial pressure of a gas?
Solubility and partial pressure are directly related.
What are standard state conditions?
Standard state conditions (298 K, 1 atm, 1 M concentrations) are used in thermodynamics and electrochemistry. (Do not confuse with STP)
Van der Waals equation of state
The a term corrects for attractive forces between molecules (will be small for small, weakly polarized molecules). The b term corrects for size (larger molecules will occupy more volume).
root-mean-square speed
The higher the temperature, the faster the molecules move. The larger the molecules, the slower they move.
Given that the gases at the center of the sun have an average molar mass of compressed to a density of under 1.30 × 109 atm of pressure, what's the temperature at the center of the sun?
The ideal gas law can be modified to include density (ρ) because the number of moles of gas, n, is equal to the mass divided by the molar mass. Thus, Isolating for temperature gives T = PM/pR
What is the density of neon at STP?
The mass of 1 mole of neon gas equals 20.2 grams. At STP, 1 mole of neon occupies 22.4 L. density = 20.2 g/mol / 22.4 L/mol = .902 g/L
What deviations from the ideal gas law happen at extremely high pressures?
The size of the molecules relative to the space between them is increased, resulting in a higher-than-ideal volume.
According to the kinetic molecular theory, what's the relationship between absolute temperature and kinetic energy?
The speed of a gas particle is proportional to its absolute temperature.
Dalton's Law of Partial Pressures
The total pressure of a gaseous mixture is equal to the sum of the partial pressures of the component gases.
At constant temperature and pressure, which occupies the most volume: 1 mole CO2, 1 mole N2, 1 mole CH4, or 1 mole of CH3Cl?
They occupy the same volume because 1 mole always equals 22.4 L.
A gas at a temperature of 27°C has a volume of 60.0 mL. What temperature change is needed to increase this gas to a volume of 90.0 mL?
Use Charles's law. Convert the temperature to kelvins. Think of this as a proportionality: If the volume is multiplied by x the temperature will also have to be multiplied by x. Final temperature is 450 K, which represents a 150 K increase (which is equivalent to an increase of 150°C).
At sea level and 25°C, the solubility of oxygen gas in water is 1.25 × 10−3 M. In Denver, a city in the United States that lies high above sea level, the atmospheric pressure is 0.800 atm. What equation should be used to calculate the solubility of oxygen in water in Denver?
Use Henry's law: he solubility of gases in liquids is directly proportional to the atmospheric pressure.
Charles's law
When pressure and number of moles are held constant, volume is directly proportional to absolute temperature. V/T = (nR/P) Since nR/P is constant, V1/T1 = V2/T2
Avogadro's principle
When pressure and temperature are held constant, there is a direct relationship between number of moles of gas and volume. n/V = k or n1/V1 = n2/V2
Gay-Lussac's law
When volume and number of moles are held constant, there is a direct relationship between temperature and pressure. P/T = k or P1/T1 = P2/T2
What do the variables of "a" and "b" represent in the Van der Waal's equation of state?
a= attractive forces constant to correct for pressure. b= bigness factor to correct for volume
Equation to calculate density of a gas
density = mass/volume = PM/RT
Graham's law
gases with lower molar masses will diffuse or effuse faster than gases with higher molar masses at the same temperature.
Gases found in the environment are most likely to exhibit properties similar to that of ideal gases under conditions of
high temperatures and low pressures, because they minimize intermolecular forces.
Atmospheric air is comprised, roughly, of 80% nitrogen and 20% oxygen. A 100 L sample of atmospheric air is kept at 300 K and 100 kPa. How many moles of oxygen molecules are found in this gas sample? (Use R = 10 (L\cdot kPa)/(mol\cdot K))(L⋅kPa)/(mol⋅K))
n= (100⋅20)/(10⋅300) = 2/3moles.
Combined gas law
shows an inverse relationship between pressure and volume and direct relationships between pressure and volume with temperature. P1V1/T1 = P2V2/T2
Henry's law
the amount of gas dissolved in solution is directly proportional to the partial pressure of that gas at the surface of a solution.
Diffusion
the spreading out of particles from high to low concentrations
Boyle's Law
the volume of a sample of gas at a given temperature varies inversely with the applied pressure. V ∝ 1/P
Effusion
when a gas moves through a small hole under pressure.