Chemistry: The Gas Phase

Question 1

Gas Phase

Answer 1

The atoms or molecules in has move rapidly and are far apart from each other. Only very weak IMF exist between gas particles; this results in certain characteristic physical properties, such as ability to expand to fill any volume and to take on the shape of a container. Furthermore, gases are easily, though not infinitely, compressible.

Question 2

Gas Pressure Units

Answer 2

1 atm = 760 mm Hg = 760 torr

Question 3

Standard Temperature and Pressure (STP)

Answer 3

273.15 K and 1 atm. Not to be confused with standard conditions (25 degrees celcius or 298 K).

Question 4

Boyle’s Law

Answer 4

Experimental studies performed by Robert Boyle in 1660 led to the formulation of Boyle’s law. His work showed that for a given gaseous sample held at constant temperature (isolthermal conditions), the volume of gas is inversely proportional to its pressure PV = K. It’s important to note that the individual values of pressure and volume can vary greatly for a given sample of gas. However, as long as the temperature remains constant and the amount of gas doesn’t change, the product of both P and V will equal the same constant (k). Subsequently, for a given gas under two sets of conditions, the following equation can be derived. P1V1 = k1 = P2V2 or simply P1V1 = P2V2 PV = k or P1V1 = P2V2 where k is a proportionality constant and the subscripts 1 and 2 represent two different sets of conditions.

Question 5

Law of Charles and Gay-Lussac

Answer 5

Or simply Charles’s law. Was developed during the early 19th century. The law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature. The absolute temperature is the temperature expressed in Kelvin, which can be calculated from the expression Tk = Tc + 273.15 V/T = k or V1/T1 = V2/T2 where k is a constant and the subscripts 1 and 2 represent 2 different sets of conditions. It’s important to note that the temperature -273.15 is the theoretical lowest attainable temperature, known as absolute zero.

Question 6

Avogradro’s Principle

Answer 6

In 1811, Amedeo Acogadro proposed that for all gases at a constant temperature and pressure, the volume of the gas will be directly proportional to the number of moles of gas present; therefore, all gases have the same number of moles in the same volume. n/V = k or n1/V1 = n2/V2 The subscripts 1 and 2 once again apply to two different sets of conditions with the same temperature and pressure.

Question 7

Ideal Gas Law

Answer 7

A theoretical gas whose volume-pressure-temperature behavior can be completely understood by the ideal gas equation is known as an “ideal gas.” The ideal gas law combines the relationships outlined in Boyle’s law, Charles’s law, and Avogadro’s principle to yield an expression that can be used to predict the behavior of a gas. The ideal gas law shows the relationship between four variables that define a sample of gas-pressure (P), volume (V), temperature (T), and number of moles (n). PV = nRT R is the gas constant. Under STP conditions, one mole of gas was shown to have a volume of 22.4 L. Substituting these values into the ideal gas equation gives R = 8.21 x 10^-2 (L x atm)/(mol x K). The gas constant may be expressed in many other units: another common value is 8.314 J/(K x mol), which is derived when SI units of Pascals (for pressure) and cubic meters (for volume) are substituted into the ideal gas law. Note: When calculating using the ideal gas law, it’s important to choose a value of R that matches units of variables.

Question 8

Density

Answer 8

The mas per unit volume of a substance and, for gases, is usually expressed in units of g/L.

Question 9

Density: Calculated Using Ideal Gas Law

Answer 9

By rearrangement, the ideal gas equation can be used to calculate the density of gas.

PV = nRT

n = m/MM

PV = (m/MM)RT

d = m/v = {P(MM)}/RT

Question 10

Density: Calculated Using STP

Answer 10

Another way to find the density of a gas is to start with the volume of a mole of gas at STP, 22.4 L, calculate the effect of pressure and temperature on the volume, and finally calculate the density by dividing the mass by the new volume.

Question 11

Density: Calculated Using P₁V₁/T₁ = P₂V₂/T₂

Answer 11

The following equation, derived from Boyle’s and Charles’s laws, is used to relate changes in the temperature, volume, and pressure of a gas. P1V1/T1 = P2V2/T2 where the subscripts 1 and 2 refer to the two states of the gas (at STP and under the actual conditions). To calculate a change in volume, the equation is rearranged as follows. V2 = V1(P1/P2)(T1/T2) V2 is then used to find the density of the gas under nonstandard conditions. d = m/V2 Visualizing how the changes in pressure and temperature affect the volume of the gas, can help you check whether or not you have accidentally confused the pressure or temperature value that belongs in the numerator with the one that belongs in the denominator.

Question 12

Molar Mass

Answer 12

Sometimes the identity of a gas is unknown, and the molar mass must be determined to identify it. Using the equation for density derived from the ideal gas law, the molar mass of a gas can be determined experimentally as follows. The pressure and temperature of a gas contained in a bulb of a given volume are measured, and the weight of the bulb plus sample is found. Then the bulb is evacuated, and the empty bulb is weighed. The weight of the bulb plus sample minus the weight of the bulb yields the weight of the sample. Finally, the density of the sample is determined by divided the weight of the sample by the volume of the bulb. The density at STP is calculated. The molecular weight is then found by multiplying the number of grams per liter by 22.4 liters per mole.

Question 13

Real Gases

Answer 13

In general, the ideal gas law is a good approximation of the behavior of real gases, but all real gases deviate from ideal gas behavior to some extent, particularly when the gas atoms of molecules are forced into close proximity under high pressure and at low temperature, so that molecular volume and intermolecular attractions become significant.

Question 14

Deviations Due to Pressure

Answer 14

As the pressure of a gas increases, the particles are pushed closer and closer together. As the condensation pressure for a given temperature is approached, intermolecular attraction forces become more and more significant until the gas condenses into the liquid state. At moderately high pressure (a few hundred atmospheres) the volume of a gas is less than would be predicted by the ideal gas law, due to intermolecular attraction. At extremely high pressure the size of the particles becomes relatively large compared to the distance between them, and this causes the gas to take up a larger volume than would be predicted by the ideal gas law.

Question 15

Deviations Due to Temperature

Answer 15

As the temperature of a gas is decreased, the average velocity of the gas molecules decreases, and the attractive IMFs become surprisingly significant. As the condensation temperature is approached for a given pressure, intermolecular attractions eventually cause the gas to condense to a liquid state. As the temperature of a gas is reduced toward its condensation point (which is the same as its boiling point), IMA (intermolecular attraction) causes the gas to have a smaller volume than would be predicted by the ideal gas law. The closer the temperature of a gas is to its boiling point, the less ideal is its behavior.

Question 16

Dalton’s Law of Partial Pressures

Answer 16

When two or more gases are found in one vessel without chemical interaction, each gas will behave independently of the other(s). Therefore, the pressure exerted by each gas in the mixture will be equal t the pressure that gas would exert if it were the only one in the container. The pressure exerted by each individual gas is called the partial pressure of the gas. In 1801, John Dalton derived an expression, which states that the total pressure of a gaseous mixture is equal to the sum of the partial pressures of the individual components. Pt = Pa + Pb + Pc + … The partial pressure of a gas is related to its mole fraction and can be determined using the following equations: Pa = PtXa Xa = na (moles of A)/nt (total moles)

Question 17

Kinetic Molecular Theory of Gases

Answer 17

As indicated by the gas laws, all gases show similar physical characteristics and behavior. A theoretical model to explain the behavior of gases was developed during the second half of the 19th century. The combined efforts of Boltzmann, Maxwell, and others led to a simple explanation of gaseous molecular behavior based on the motion of individual molecules. This model is called the kinetic molecular theory of gases. Like the gas laws, this theory was developed in reference to ideal gases, although it can be applied with reasonable accuracy to real gases as well.

Question 18

Assumptions of the Kinetic Molecular Theory

Answer 18

• Gases are made up of particles whose volumes are negligible compared to the container volume.
• Gas atoms or molecules exhibit no IMAs or repulsions.
• Gas particles are in continuous, random motion, undergoing collisions with other particles and the container walls.
• Collisions between any two gas particles are elastic, meaning that there’s no overall gain or loss of energy.
• The average kinetic energy of gas particles is proportional to the absolute temp of the gas and is the same for all gases at a given temp.

Question 19

Average Molecular Speeds

Answer 19

According to the kinetic molecular theory of gases, the average kinetic energy of a gas particle is proportional to the absolute temperature of gas: KE = (1/2)mv^2 = (3/2)kT where k is the Boltzmann constant. This equation also shows that the speed of a gas molecule is related to its absolute temperature. However, because of the large number of rapidly and randomly moving gas particles, the speed of an individual gas molecule is nearly impossible to define. Instead, it is the average speed of all the gas particles that can be related exactly to the temperature. Some particles will be moving at higher speeds and some at lower speeds.

Question 20

Maxwell-Boltzmann Distribution Curve

Answer 20

Shows the distribution of speeds of gas particles at a given temperature. The bell-shaped curve flattens and shifts to the right as the temperature increases, indicating that at higher temperatures, more molecules are moving at high speeds.

Question 21

Diffusion

Answer 21

Diffusion of gases can provide a demonstration of random motion when the molecules of these gases mix with one another by virtue of their individual kinetic properties. Diffusion occurs when gas molecules diffuse through a mixture. Diffusion accounts for the fact that an open bottle of perfume can quickly be smelled across a room. The kinetic molecular theory of gases predicted that heavier gas molecules diffuse more slowly than lighter ones because of their differing average speeds. In 1832, Thomas Graham showed mathematically that under isothermal and isobaric conditions, the rates at which two gases diffuse are inversely proportional to the square root of their molar masses. Thus: r1/r2 = [(MM2)/MM1)]^(1/2) = Square root of {MM2)/(MM1) where r1 and MM1 represent the diffusion rate and molar mass of gas 1, and r2 and MM2 of gas 2.

Question 22

Effusion

Answer 22

Flow of gas particles under pressure from one compartment to another through a small opening. Graham used the kinetic molecular theory of gases to show that for two gases at the same temperature, the rates of effusion are proportional to the average speeds. He then expressed the rates of effusion in terms of molar mass and found that the relationship is the same as that for diffusion. e1/r2 = [(MM2)/(MM1)]^(1/2)