Gases

Ideal Gas Assumptions

1) molecules of an ideal gas do not attract or repel each other 2) particles of an ideal gas occupy no volume 3) collisions are perfectly elastic

Kinetic Molecular Theory of Gases

1) the pressure on the walls of the container is a result of elastic collision of particles with the wall 2) the average KE of particles is directly proportional to temperature of the gas

According to Avogadro's law, how many liters does one mole of gas occupy at STP?

22.4 L

The kinetic molecular theory of gases states that the average KE of one mole of any gas is proportional to

3/2 RT

Standard Temperature and Pressure (STP)

A temperature of 273 K and a pressure of 1.00 atm

Standard conditions

A temperature of 298 K, a pressure of 1 x 10^5 Pa, and all ion solutions having a concentration of 1 M.

A sample of gas is held at 1 atm and its volume is measured at 2 L. If the pressure on the gas were increased to 2 atm, what would be the new volume? Assume all other conditions remain constant.

At a constant temperature, Boyle's law relates the volume and pressure of a gas as follows: P1V1 = P2V2. Therefore, if the pressure were doubled, the volume would halve.

Which pair of gases is most likely to produce ideal gas-like behavior? A) HCl and NaOH B) HF and NaOH C) HCl and CH4 D) HF and CH4

C The most ideal gases are those that experience the weakest intermolecular forces. HCl and CH4 have the least polar bonds of the gases listed and thus will exert the weakest attractive forces on other molecules.

A balloon is inflated until its volume reaches 2 L. Assuming all else is held constant, what would happen to the balloon's volume if it were moved to a colder environment?

Charles' law states that as temperature increases, volume also increases. Therefore, if temperature decreases, the volume of the balloon should also decrease.

A sealed flask is filled with three gases: 0.5 mol ammonia, 0.25 mol oxygen, and 0.75 mol helium. If the partial pressure of NH3 is 415 torr, what is the total pressure in the flask?

Dalton's law states that the total pressure in a vessel is the sum of the partial pressures of the components. Moreover, the partial pressure of a gas is proportional to its mole fraction in the container. We already know that the total number of moles in the flask is 0.5 + 0.25 + 0.75 = 1.5 moles. Since exactly one-third of this is ammonia, the total pressure is 3*415 torr, or 1245 torr.

A sealed flask is filled with three gases: carbon dioxide, oxygen, and helium. The total pressure in the flask is 4 atm. The partial pressure of helium is 1 atm and the partial pressure of oxygen 2 atm. What is the mole fraction of carbon dioxide?

Dalton's law states that the total pressure in a vessel is the sum of the partial pressures of the components. Moreover, the partial pressure of a gas is proportional to its mole fraction in the container. We are told that the total pressure is 4 atm and 3 atm are due to helium and oxygen. Thus, CO2's partial pressure is 1 atm. Since the mole fraction is proportional to partial pressure / total pressure, the mole fraction of CO2 must be ¼. We can't determine how many moles there are without more information, but we do know that ¼ of the total moles will be CO2.

Gas A, a compound used in industrial cleaning, is observed to diffuse through a room at approximately 0.1 m/s. If helium gas diffuses through the same room at 0.8 m/s, the molar mass of Gas A is:

Graham's law can be used to compare the rates of diffusion of two gases. This equation can be written as rate 1 / rate 2 = √molar mass 2 / √molar mass 1; in other words, the rate of diffusion of a gas varies with the reciprocal of the square root of its molar mass. Here, let's give helium "Rate 1" and our unknown gas "Rate 2." This equation becomes 0.8 m/s / 01. m/s = √molar mass 2 / √4g/mol, and the molar mass of Gas A can be calculated at 256 g/mol.

Rank the following molecules from smallest to largest b factor from the Van der Waals equation. O2,H2,CO2

H2 < O2 < CO2

Sodium bicarbonate, a commonly used antacid, produces carbon dioxide and salt water when mixed with hydrochloric acid in the gut. The reaction for this process is as follows: HCl (aq) + NaHCO3 (aq) → H2O (l) + CO2 (g) + NaCl (aq) 250 mL of 2 M HCl is mixed with excess sodium bicarbonate in a closed container and allowed to react. If the carbon dioxide produced is then transferred to a glass vessel with 0.5 mol water vapor and 0.5 mol gaseous ammonia, what will be the mole fraction of CO2 in the vessel?

Here, mole fraction can be calculated as the number of moles of carbon dioxide present divided by the total moles of gas. 250 mL HCl × (2 mol HCl / 1000 mL) × (1 mol CO2 / 1 mol HCl) = 0.5 mol CO2. To find our answer, take 0.5 mol CO2 / 1.5 total moles in the vessel = 0.33.

ideal gas law

PV=nRT

Dalton's Law equation

Pgas = Xgas * Ptot

Graham's Law Equation

Rate 1/Rate 2= square root of molar mass 2/ square root of molar mass 1

A biologist is making a variety of measurements for a sample of CO2 generated by a colony of aerobic bacteria. The sample contains exactly 1 mole of gas and is being held in a 0.05 L container. When the biologist calculates the PV/ RT ratio of the gas, he finds that it is 1.05. How could this finding be explained?

Since the sample contains 1 mole of gas, we can rearrange the ideal gas law to find our expected PV/RT ratio: 1. The given value is higher, implying that either pressure or volume is larger than expected. For the ideal gas law to work properly, two main assumptions are necessary: that the volume of particles themselves is negligible and that no intermolecular forces are present between particles. However, these assumptions become especially untrue at low temperature and high pressure. Classically, we think of low temperatures systems being significantly moved away from ideal gas behavior by intermolecular forces, and high pressure systems as being influenced primarily by intermolecular collisions.

What is the volume of a sample of 2 moles of a gas, held at 2 atm and 0°C. (Note: R = 0.08 L atm / mol K)

This problem can be solved using the ideal gas law: PV=nRT, which we can convert to V = nRT/P. Calculation will yield 22.4 L. Note, also, that 1 mole at 1 atm and 0°C occupies 22.4 L. Held at 2 atm, with all else the same, the volume will be 11.2 L. So 2 moles at 2 atm will occupy 22.4 L.

True or false: If Gas A diffused 5 times faster than Gas B, then Gas B must have 25 times the molar mass.

This statement is true. Graham's law can be used to compare the rates of diffusion of two gases. This equation can be written as rate 1 / rate 2 = √molar mass 2 / √molar mass 1; in other words, the rate of diffusion of a gas varies with the reciprocal of the square root of its molar mass. So, if Gas A diffused 5 times faster than Gas B, then the molar mass of Gas B must be 5^2 = 25 times greater.

Dalton's Law

at constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases

Which of the following scenarios violate the assumptions underlying the ideal gas law? Choose all that apply. a) two gas particles collide elastically b) two gas particles end up stuck together due to H-bonding c) two gas particles collide inelastically d) two gas particles occupy different different amount of space

b,c,d

According to the assumptions of the ideal gas law, gas particles can collide, but those collisions are _______

elastic and result in no net energy loss

Avogadro's law

equal volumes of gases at the same temperature and pressure contain equal numbers of molecules volume and moles of gas are directly proportional

Charle's Law

gas temperature and volume are directly proportional

Gases behave least ideally at

high pressure and low temperature

which conditions favor ideal gas behavior

high temperature low pressure large volume

Boyle's Law

pressure and volume of an ideal gas are inversely proportional if temperature is constant

A red balloon is filled with ⅛ mole of CO2, a blue balloon with ½ mole of CO2, a yellow balloon with ¼ mole of CO2, and a green balloon with ⅓ mole of CO2. Assuming all the balloons are held at STP, rank them in order of smallest to largest volume.

red balloon yellow balloon green balloon blue balloon Avogadro's Law --> number of moles is directly proportional to volume

Graham's law of effusion

states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass

Graham's Law is derived from

temperature is proportional to kinetic energy

The b factor in the Van der Waals equation relates to

the volume of the gas molecule

Under the kinetic molecular theory, the pressure of a sample of gas comes from collisions between gas particles and ______.

the walls of the container

True or false: Oxygen would be expected to effuse more quickly than carbon dioxide.

true. Graham's law states that both the effusion rate and the diffusion rate are directly proportional to the reciprocal of the square root of the molar mass of a gas. Thus, as molecular mass increases, the effusion rate decreases. Since oxygen has a smaller molar mass than carbon dioxide, it would be expected to effuse more quickly.

which equation is used for real gases and why

van der waals equation, to account for attractive forces between molecules and the size of the molecules