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 changing two of these variables affects 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 conditions (initial and final) are compared.

• Example: If a sample of helium gas changes in volume and pressure, the Combined Gas Law can determine the new temperature.

Avogadro’s Law: Volume and Moles

Avogadro’s Law describes the direct relationship between the volume of a gas and the number of moles, when 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 calculate changes in volume when the amount of gas changes.

• Example: Adding more helium to a weather balloon increases its volume proportionally.

Standard Temperature and Pressure (STP)

STP is a set of standard 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 gas = 22.4 L at STP

• Conversion Factors: $\frac{22.4\text{ L}}{1\text{ mole gas}}$ and $\frac{1\text{ mole gas}}{22.4\text{ L}}$

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

Molar Mass

Molar Mass of Elements

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 all elements in the formula, multiplied by their respective subscripts.

• 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 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	Relates changes in pressure, volume, and temperature
Avogadro’s Law	$\frac{V_1}{n_1} = \frac{V_2}{n_2}$	V, n	Relates volume and moles of gas
STP	1 mole = 22.4 L	n, V	Standard conditions for gases
Dalton’s Law	$P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$	P	Total pressure in gas mixtures
Molar Mass	Sum of atomic masses	g, mol	Converts between mass and moles