Ideal Gas law

The Ideal Gas law interrelates pressure, temperature, volume and number of moles of a gas sample. This law integrates the laws of Boyle, Charles and Avogadro.

Boyle's law : V ∞ 1/P
Charles' law: V ∞ T
Avogadro's law: V ∞ n

Combining these three laws will yield to a more general equation:

PV = nRT

where R is the gas constant:

R = 0.0821 L.atm / mol.K

Sample Problem:

What volume will1.27 moles of Helium gas occupy at STP?

Given:

P = 1 atm

V = ?

n = 1.27mol

R = 0.0821 L.atm / mol.K

T = 25 ºC + 273 = 298K

Solution:

PV = nRT

(1 atm)V = (1.27mol)(0.0821 L.atm/mol.K)(298K)

V = (1.27mol)(0.0821 L.atm/mol.K)(298K)

(1 atm)

V = 31.07 Liters

Exercises:

1. How many moles of gas are contained in a 50.0L cylinder at a pressure of 100.0atm and a temperature of 35.0ºC?
2. What would be the volume occupied by a 1mole gas at STP?

Gay-Lussac's Law

This relationship between pressure and temperature was studied by Joseph Louis Gay-Lussac, a French Chemist. This law states that pressure is directly proportional to the absolute temperature when volume and amount of gas is held constant.
This law is mathematically expressed as:

P1 = P2

T1 T2

Sample Problem:

A sample of gas at 3000mm Hg inside a steel tank is cooled from500ºC to 0ºC. What is the final pressure of the gas inside the steel taank?

Given:

P1 = 3000 mm Hg

T1 = 500ºC + 273 = 773K

P2 = ?

T2 = 0ºC + 273 = 273K

Solution:

P1 = P2
T1 T2

(3000 mm Hg) = P2

(773K) (273K)

P2 = (3000 mm Hg)(273K)

773K

P2 = 1,059.51 mm Hg

Exercises:

1. A gas sample has a pressure of 950 torr at 120ºC. What is the final pressure of the gas after the temperature is dropped to 10ºC?
2. Pressure of a gas in a 10.0L steel cylinder is 890torr at 56ºC. To what temperature should the gas be cooled in order to reduce the pressure to 760 torr?

Combined Gas Law

The Combined Gas Law integrates the Boyle's and Charles' Law as one. This gives the relationship between temperature, pressure and volume considering the amount of gas in held constant.

It states that "for a given mass of gas, the volume is inversely proportional to the pressure and directly proportional to its absolute temperature".

Derived from Boyle's law:

P1V1 = P2V2

and Charles' law:

V1 = V2

T1 T2

will give us the Cobined Gas Law Equation:

P1V1 = P2V2

T1 T2

Sample Problem #1:

A gas occupies a volume of 3 liters at 50 degrees Celcius and 1.50 atm. Compute its volume at 25 degrees C and 1 atmosphere.

Given:

P1 = 1.50atm

V1 = 3 L

T1 = 50ºC + 273 = 323K

P2 = 1 atm

V2 = x

T2 = 25ºC + 273 = 298K

Solution:

P1V1 = P2V2
T1 T2

(1.50atm)(3L) = (1atm)V2

323K 298K

V2 = (1.50atm)(3L)(298K)

(323K)(1atm)

V2 = 4.15 liters

Sample Problem #2:

A quantity of gas exerts a pressure of 2.4atm when its volume is 4.0L at 40ºC. Calculate the pressure exerted by the same gas if the temperature is raised to 50ºC and the volume is reduced to 1.5 liters.

Given:

P1 = 2.4 atm

V1 = 4.0 L

T1 = 40ºC + 273 = 313K

P2 = ?

V2 = 1.5 L

T2 = 50ºC + 273 = 323K

Solution:

P1V1 = P2V2

T1 T2
(2.4 atm)(4.0 L) = P2 (1.5 L)
313K 323K
P2 = (2.4 atm)(4.0L)(323K)
(313K)(1.5 L)
P2 = 6.60 atm

STP = Standard Temperature and Pressure

These are standard sets of conditions for experimental measurements to allow comparisons between sets of data. These measurements are usually that of the International Union of Pure ans Applied Chemistry (IUPAC).

Standard Temperature = 25ºC

Standard Pressure = 1 atm

Exercises:

1. A gas sample occupies a volume of 20m3at 40ºC and at a pressure of 1.60 atm. What volume will it occupy at STP?
2. A certain amount of gas has a volume of 85cm3 at a temperature of 15ºC and a pressure of 800 torr. Calculate its temperature, in Kelvin, if the volume is increased to 120cm3 annd the pressure is changed to 700 torr.
3. A gas has a volume of 38 Liters at 10ºC and a pressure of 1.24atm. At what pressure will its volume be 50 Liters if the temperature is increased to 25ºC?

Charles' Law

Charles' law is also known as Temperature-Volume Relationship. This law was studied by Jacques Charles in 1787 using a balloon.

This law states that if temperature is increased, the volume of the gas will increase. Volume is directly proportional to temperature if the pressure is kept constant.

Charles' law can be mathematically expressed as:

V1/T1 = V2/T2

where:

• V1 = initial volume
• T1 = initial temperature (in Kelvin)
• V2 = final volume
• T2 = final temperature (in Kelvin)

Problem Solving Reminders:

• Analyze the given problem.
• List down the given values and what is asked.
• Identify the formula to be used.
• Write your solutions clearly.
• Analyze if your answer is theoritically correct.

Sample Problem #1:
A balloon has a volume of 2500.0 mL on a day when the temperature is 30.0ºC. If the temperature at night falls to 10.0ºC, what will be the volume of the balloon if the pressure remains constant?

Sample Problem #2:
Find the final temperature of a 2.00-L gas sample at 20.0ºC compressed to a volume of 1.00-L.

Boyle's Law

Boyle's law is one of the gas laws that illustrates the relationship between pressure and volume of gases at constant temperature. This law was analyzed by Robert Boyle in 1662. In his experiment, he varied the pressure and observed its effect on the volume of the gas without changing its temperature.

This law states that if a pressure of a gas is increased, the volume of the gas is decreased. Study the following figures.

This law can be mathematically expressed as:

P1V1=P2V2

where:

• P1 = initial pressure
• V1 = initial volume
• P2 = final pressure
• V2 = final volume

Any units of pressure and volume may be used. However, uniformity must be observed.

Pressure Units

• 1 atmosphere (atm) = 760mm Hg = 760 torr = 150000 Pascal (Pa)

Volume Units

• 1 Liter = 1000 mL
• 1mL = 1 cm3

Problem Solving Reminders:

• Analyze the given problem.
• List down the given values and what is asked.
• Identify the formula to be used.
• Write solutions clearly.
• Analyze if you have the correct answer.

Sample Problem #1:

Two hundred milliliter of gas is contained in a vessel under a pressure of 850mm Hg. What would be the new volume of the gas if the pressure is changed to 1000mm Hg?

• 
  Given:
  P1= 850 mm Hg
  V1= 200 cm3
  P2= 1000 mm Hg
  V2= ?
  Equation: P1V1 = P2V2
• Solution:
  P1V1 = P2V2
  (850mm Hg)(200cm3)=(1000mm Hg) V2
  (850mm Hg)(200cm3)= V2
  (1000mm Hg)
  170 cm3 = V2

Sample Problem #2:

A 2.5 liter sample of a gas is collected at a pressure of 1.25 atm. Calculate the pressure needed to reduce the volume of a gas to 2.0 liters. The temperature remains unchanged.

• Given:
  P1= 1.25 atm
  V1= 2.5 liter
  P2= ?
  V2= 2.0 liters
  Equation: P1V1 = P2V2
• 
  Solution:
  P1V1 = P2V2
  (1.25 atm)(2.50 L) = P2 (2.0 L)
  (1.25 atm)(2.50 L) = P2
  (2.0L)
  P2 = 1.56 atm

Gases

According to the philosopher Anaximenes, matter exists from air. Gases are classified as the third physical state of matter. Like everything, each one is different from the rest and it has its own characteristics. The Kinetic Molecular Theory of Gases, postulates based from basic behaviors of atoms, attempts to explain the properties of gases. The Kinetic Molecular Theory, also called as the Collision Theory has the following postulates:

1. Gases are composed of atoms/molecules that are separated and far from one another. The space betweenn them is very wide, thus, occupying a wide space in the atmosphere.
2. These tiny particles are moving constantly in a straight path but random direction, resulting to the collision between them and with the walls of the container, thus, creating pressure.
3. The force of attraction between atoms is negligible.
   Collision of the particles does not result in the energy change, although a transfer of energy may occur in the collision.
4. All gas molecules have the same average kinetic energy at the same temperature. Temperature is defined as avergae kinetic energy. (Brown et al 2000 1)

From these postulates, we can then draw the following properties:

• Gases are compressible. Since gas molecules are from from each other, they can be compressed closer to decrease the gap between molecules.
• Gases have low densities. Since gas molecules are from from each other, they would occupy a greater space compared with the other states of matter. Gases would have lighter mass to keep moving at a particular speed. With a small value of mass, and occupying a big volume, the ration (density) would be low.
• Gases exert pressure. Gas molecules are constantly moving, hitting everything in its path thus creating pressure.
• Gases diffuse easily. Since gas molecules move constantly, it then travels from one place to another.
  Gases are affected by changes in temperature. (2)

Aside from the behavioral properties, gases also have the following measurable properties:

• Pressure (P). A measure of force applied on an object per unit area (P=F/A). Pressure in the atmosphere is caused by the weight of the air from the outer edge of the atmosphere down to the surface of the earth. Measurement of pressure was first introduced by Evangelista Toricelli.
• Temperature (T). The average kinetic energy. If a gas is to reach absolute zero (O Kelvin), its particles would have no energy or motion.
• Volume (V). Volume of a gas is equal to the volume of the container since a gas completely fills its container.
• Amount of gas (n). The amount of gas is measured in moles or number of particles.

Other properties:

• Diffusion. the process of spreading out of molecules to fill a space uniformly.
• Effusion. the process by which gas molecules spread out in an empty space through a small opening.