INTRO CHEMISTRY I CHEM 1305

GAS LAWS

• Expansion - gases expand indefinitely and uniformly to fill all the space in which they are placed.
• Indefinite Shape and Volume - gas has no definite shape or volume, but will fit the vessel in which it is placed.
• Compressibility - gases can be highly compressed.
• Low density - density of gases is very low and, therefore, measured in grams/liter (g/l)
• Diffusion - two or more different gases will normally mix completely and uniformly when in contact with each other.

• No attractive forces exist between the molecules in a gas.

• The molecules are in a state of constant, rapid motion, with each other and the walls of the container.

• All collisions are perfectly elastic (no loss of energy in collision) therefore, the molecules do not slow down after collision.

• The average kinetic energy is proportional to the temperature in kelvins. The higher the temperature, the more motion.

The above conditions are called IDEAL GASES.

Boyle's Law

Boyles Law - at constant temperature, the volume is inversely proportional to the pressure.

As the pressure increases, the volume decreases

As the pressure decreases, the volume increases

Example: A gas has a volume of 2 liters at a pressure of 6 atm.  Calculate the new volume if the pressure was decreased to 3 atm and the temperature remained the same. In Boyle's Law, the volume is inversely proportional to the pressure.  Therefore, if the pressure is reduced by half, the volume would be expected to double.

Charles's Law

Charles Law - at constant pressures the volume is directly proportional to the temperature.

As the temperature increases, the volume increases

As the temperature decreases, the volume decreases

Example: A gas has a volume of 2 liters at a temperature of 600 K.  Calculate the new volume if the temperature was decreased to 300 K and the pressure remains the same. In Charles's Law, the volume is proportional to the temperature.  Therefore, if the temperature is reduced by half, the volume would be expected to half.

Gay-Lussac's Law

Gay-Lussac Law - at constant volume, the pressure is directly proportional to the temperature.

As the temperature increases, the pressure increases

As the temperature decreases, the pressure decreases

Example: A gas has a pressure of 700 torr at a temperature of 300 K.  Calculate the new pressure if the temperature was increased to 600 K and the volume remains the same. In Gay-Lussac's Law, the pressure is proportional to the temperature.  Therefore, if the temperature is doubles, the pressure would be expected to double.

General Gas Law

Boyles and Charles Law can be combined into a single equation.

Example:   solve for pressure 2 liters of a gas has an initial pressure of 800 torr at a temperature of 300 K.  What would be the new pressure if the temperature was increased to 600 K and the volume remained the same? Solution: 1.  Using the general gas law formula, solve for P2 2.  Make a list of the variables, and fill in the table. P1 = 800 torr P2 = ? V1 = 2 liter V2 = 2 liter T1 = 300 K T2 = 600 K 3.  Using the equation for P2 , fill in the variables and solve. Since the volume remained the same and the pressure is proportional to the volume, the pressure would be expected to double if the temperature doubled.

 

Example:   solve for temperature A gas has an initial pressure of 4 atm at a temperature of 300 K with an initial volume of 2 liters.  What would be the new temperature if the pressure was increased to 8 atm and the volume doubled? Solution: 1.  Using the general gas law formula, solve for T2 2.  Make a list of the variables, and fill in the table. P1 = 4 atm P2 = 8 atm V1 = 2 liter V2 = 4 liter T1 = 300 K T2 = ? 3.  Using the equation for T2 , fill in the variables and solve. Since pressure and volume are proportional to the temperature, if both the pressure and the volume each doubled, the temperature would be expected to increase by a factor of 4.

 

Example:   solve for volume A gas has an initial pressure of 30 psi at a temperature of 600 K with an initial volume of 2 liters.  What would be the new volume if the pressure was decreased to 15 psi and the temperature remained the same? Solution: 1.  Using the general gas law formula, solve for V2 2.  Make a list of the variables, and fill in the table. P1 = 30 psi P2 = 15 psi V1 = 2 liter V2 = ? T1 = 600 K T2 = 600 K 3.  Using the equation for T2 , fill in the variables and solve. Since the temperature remained the same and the pressure is inversely proportional to the volume, the volume would be expected to double if the pressure halved.

click here to practice combined gas law problems.

Ideal Gas Law

Example: solve for moles A gas has a pressure of 4 atm at a temperature of 300 K with an initial volume of 2000 ml.  Calculate the moles of the gas. Solution: 1.  Using the ideal gas law formula, solve for moles. 2.   Convert all units to either atm, liters, or kelvin. 3.  Make a list of the variables, and fill in the table. P = 4 atm R = 0.0821 V = 2 liter n = ? T = 300 K 4.  Using the equation for moles , fill in the variables and solve.

 

Example:   solve for pressure 2 moles of a gas has a volume of 0.75 liters at a temperature of 27 oC.  Calculate the pressure of the gas. Solution: 1.  Using the ideal gas law formula, solve for pressure. 2.   Convert all units to either atm, liters, or kelvin. 3.  Make a list of the variables, and fill in the table. P = ? R = 0.0821 V = 0.75 liter n = 2 moles T = 300 K 4.  Using the equation for pressure, fill in the variables and solve.

 

Example: solve for the gas constant 1 mole of a gas at STP (273 K and 1 atm) has a volume of 22.4 liters.  Calculate the gas constant R. Solution: 1.  Using the ideal gas law formula, solve for the gas constant R. 2.  Make a list of the variables, and fill in the table. P = 1 atm R = ? V = 22.4 liter n = 1 moles T = 273 K 3.  Using the equation for R , fill in the variables and solve.

 

Example:   solve for temperature Nitrogen gas (N2 - 28 amu) has a volume of 5 liters, a pressure of 15 atm and a mass of 56 grams.  Calculate the temperature of the gas. Solution: 1.  Using the ideal gas law formula, solve for temperature. 2.   Convert grams to moles. 3.  Make a list of the variables, and fill in the table. P = 15 atm R = 0.0821 V = 5 liter n = 2 moles T = ? g = 56 grams 4.  Using the equation for R , fill in the variables and solve.

 

Example:   solve for volume A gas has a temperature of 300 K, a pressure of 22 psi and 2 moles.  Calculate the volume of the gas. Solution: 1.  Using the ideal gas law formula, solve for volume. 2.   Convert all units to either atm, liters, or kelvin. 3.  Make a list of the variables, and fill in the table. P = 1.5 atm R = 0.0821 V = ? n = 2 moles T = 300 K 4.  Using the equation for volume, fill in the variables and solve.

 

Example:   solve for mass Chlorine gas (Cl2 - 71 amu) has a volume of 2 liters, a pressure of 4 atm and a temperature of 300 kelvin.  Calculate the mass of chlorine. Solution: 1.  Using the ideal gas law formula, solve for moles. 2.  Make a list of the variables, and fill in the table. P = 4 atm R = 0.0821 V = 2 liter n = ? T = 300 K g = ? 3.  Using the equation for moles , fill in the variables and solve for moles. 4.  Put moles into the table. P = 4 atm R = 0.0821 V = 2 liter n = 0.32 moles T = 300 K g = ? 5.  Using the formula to convert grams to moles, calculate the grams of chlorine. grams = moles x mol wt grams = 0.32 moles x 71 amu = 22.7 grams

click here to practice idea gas law problems.

Dalton's Law of Partial Pressures

Daltons Law of Partial Pressures - each gas in a mixture exerts a partial pressure equal to the pressure it would exert if it was the only gas present.  The sum of all the partial pressures of all the gas is equal to the total pressure.

Example: A mixture of gases has the following partial pressures: H2 = 3 atm  N2 = 2 atm  O2 = 10 atm.  Calculate the total pressure of the system.

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Gas Law Quiz