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: Calculating the new temperature when volume and pressure change for a sample of helium gas.

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 volume changes as the amount of gas changes.

• Example: Calculating the final volume of a weather balloon when more helium is added.

Standard Temperature & Pressure (STP)

STP is a set of conditions used for comparing gases. At STP, 1 mole of any gas occupies a molar volume of 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: $\text{22.4 L (STP)} \leftrightarrow \text{1 mole gas}$

• 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 for elements

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 moles (subscript) in the formula.

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

• Example: Calculating the molar mass of Li2CO3 by summing the masses of 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: Determining the partial pressure of helium in a scuba tank mixture when the total pressure and oxygen partial pressure are known.

Practice Problems

• Combined Gas Law: Calculate the new temperature for a helium sample when volume and pressure change.

• Avogadro’s Law: Find the final volume of a weather balloon after adding more helium.

• Molar Mass: Calculate the molar mass of C2H6O.

• STP Volume: Determine the volume at STP for 4.00 g of CH4.

• Dalton’s Law: Find the partial pressure of helium in a gas mixture for scuba diving.

Additional info: These notes cover Chapter 8, sections 8.5–8.7, which are directly relevant to GOB Chemistry topics on gases, molar mass, and gas mixtures.