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

Gas Laws

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 describes the direct relationship between the volume of a gas and the number of moles present, assuming constant temperature and pressure.

• 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: A weather balloon’s volume increases as more helium is added, calculated using Avogadro’s Law.

Standard Temperature & Pressure (STP)

STP is a set of conditions used for comparing gases. At STP, 1 mole of any 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: $\frac{22.4\text{ L}}{1\text{ mole}}$ and $\frac{1\text{ mole}}{22.4\text{ L}}$

• Application: Used to convert between moles and volume for gases at STP.

Molar Mass

Molar Mass of Elements

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

• Definition: The mass of 1 mole of an element (in grams)

• Example: 1 mole of carbon atoms (C) has a mass of 12.01 g

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

Molar Mass of Compounds

The molar mass of a compound is calculated by summing the molar masses of each element, multiplied by their respective subscripts in the chemical formula.

• Steps:

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

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

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

• Example: For Li2CO3, calculate the molar mass by summing the contributions from Li, C, and O.

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 individual gas. 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 in a mixture or the partial pressure of a component gas.

• 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	1 mole = 22.4 L	n, V	Standard comparison for gases
Molar Mass	Sum of (atomic mass × subscript)	g, mol	Converts mass to moles
Dalton’s Law	$P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$	P	Total pressure in mixtures