Gas Laws, Molar Mass, and Dalton’s Law: GOB Chemistry Study Notes

Gas Laws and Calculations

The Combined Gas Law

The Combined Gas Law integrates the relationships between pressure, volume, and temperature for a fixed amount of gas. It is useful for predicting how changes in two variables affect the third, provided the number of moles remains constant.

• Formula: $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

• Variables: P = pressure, V = volume, T = temperature (in Kelvin)

• Application: Used to solve problems where two of the three variables change and the amount of gas is constant.

• Example: If a sample of helium gas changes volume and pressure, the new temperature can be calculated using the formula above.

Avogadro’s Law: Volume and Moles

Avogadro’s Law states that the volume of a gas is directly proportional to the number of moles, provided temperature and pressure are constant.

• Formula: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Variables: V = volume, n = number of moles

• Application: Used to determine how the volume changes when the amount of gas changes.

• Example: If a weather balloon is filled with more helium, its volume increases proportionally.

Standard Temperature and Pressure (STP) and Molar Volume

STP Conditions and Molar Volume

Standard Temperature and Pressure (STP) is a reference point for comparing gases. At STP, 1 mole of any ideal gas occupies 22.4 L.

• STP Conditions: Temperature = 273 K (0°C), Pressure = 1 atm (760 mmHg)

• Molar Volume: 1 mole of gas = 22.4 L at STP

• Conversion Factors:

  • 22.4 L (STP) per 1 mole gas

  • 1 mole gas per 22.4 L (STP)

Molar Mass and Calculations

Molar Mass of Elements

The molar mass is the mass of 1 mole of an element, expressed in grams. It is numerically equal to the atomic mass from the periodic table.

• Definition: Molar mass = mass of 1 mole of an element (g)

• Example: 1 mole of carbon atoms = 12.01 g

• Application: Used to convert between grams and moles in chemical calculations.

Molar Mass of Compounds

To determine the molar mass of a compound, sum the molar masses of each element multiplied by their subscripts in the formula.

• Steps:

  1. Obtain the molar mass of each element from the periodic table.

  2. Multiply each molar mass by the number of moles (subscript) in the formula.

  3. Add the masses for each element to get the total molar mass.

• Example: For Li2CO3:

  • Li: 2 × 6.941 g = 13.88 g

  • C: 1 × 12.01 g = 12.01 g

  • O: 3 × 16.00 g = 48.00 g

  • Total molar mass = 13.88 g + 12.01 g + 48.00 g = 73.89 g

Dalton’s Law of Partial Pressures

Partial Pressures in Gas Mixtures

Dalton’s Law states that the total pressure of a gas mixture is the sum of the partial pressures of each gas present. Each gas in a mixture behaves independently and contributes to the total pressure.

• Formula: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Application: Used to calculate the total pressure or the partial pressure of a component in a gas mixture.

• Example: In scuba diving, the total pressure is the sum of the partial pressures of helium and oxygen.

Summary Table: Gas Laws and Molar Mass

Law/Concept	Formula	Variables	Application
Combined Gas Law	$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$	P, V, T	Predicts changes in gas conditions
Avogadro’s Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	V, n	Relates volume to moles
STP & Molar Volume	1 mole = 22.4 L at STP	n, V	Standard reference for gases
Molar Mass	Sum of (element mass × subscript)	g, mol	Converts grams to moles
Dalton’s Law	$P_{\text{total}} = P_1 + P_2 + \ldots$	P	Total pressure in mixtures

Additional info: The periodic table is essential for determining atomic and molar masses, which are foundational for stoichiometric calculations in chemistry.