Quiz 6 Things to Know

Chapter 10: Properties of Gases and Gas Laws

Relationships Among Pressure, Volume, and Temperature

Understanding the behavior of gases involves studying the relationships between pressure (P), volume (V), and temperature (T). These relationships are described by several fundamental gas laws.

• Boyle's Law: At constant temperature, the pressure of a gas is inversely proportional to its volume. $P_1V_1 = P_2V_2$

• Charles's Law: At constant pressure, the volume of a gas is directly proportional to its temperature (in Kelvin). $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Avogadro's Law: At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Ideal Gas Law: Combines the above relationships into one equation. $PV = nRT$

Example: If the pressure on a 2.0 L sample of gas is doubled at constant temperature, the volume will decrease to 1.0 L.

Velocity Distribution of Gas Molecules (Boltzmann Distribution)

The Boltzmann distribution describes the spread of molecular speeds in a gas sample at a given temperature. At low temperatures, most molecules move slowly; at high temperatures, more molecules move quickly.

• The graph of the distribution is skewed right, with a peak at the most probable speed.

• X-axis: molecular speed or kinetic energy; Y-axis: number of molecules.

• At higher temperatures, the peak flattens and shifts right, indicating higher average speeds.

Example: At room temperature, oxygen molecules have a range of speeds, but most travel near the most probable speed.

Root Mean Square Speed (urms)

The root mean square speed is a measure of the average speed of gas molecules, weighted by the square of their velocities.

• Units: meters per second (m/s).

• Formula: $u_{rms} = \sqrt{\frac{3RT}{M}}$ where R is the gas constant, T is temperature in Kelvin, and M is molar mass in kg/mol.

• Interpretation: Higher temperature or lower molar mass increases urms.

Example: Calculate urms for nitrogen gas at 300 K.

Diffusion and Effusion of Gases

Diffusion is the mixing of gases due to molecular motion; effusion is the escape of gas through a small hole. The rates depend on molar mass and temperature.

• Graham's Law of Effusion: $\text{Rate}_1/\text{Rate}_2 = \sqrt{M_2/M_1}$

• Lower molar mass gases effuse and diffuse faster.

• Practice comparing rates using the formula above.

Example: Hydrogen effuses faster than oxygen due to its lower molar mass.

Nonideal Gases

Real gases deviate from ideal behavior under high pressure and low temperature. These deviations are due to intermolecular forces and the finite volume of molecules.

• Ideal gas law assumes no interactions and negligible volume.

• Nonideal behavior is explained by the van der Waals equation:

$\left(P + a\frac{n^2}{V^2}\right)(V - nb) = nRT$

• a corrects for intermolecular attractions; b corrects for molecular volume.

Example: CO2 at high pressure shows nonideal behavior due to strong intermolecular forces.

Chapter 5: Thermodynamics and Calorimetry

Energy, Work, and Conservation of Energy

Thermodynamics studies energy changes in chemical systems. Kinetic energy is energy of motion; potential energy is stored energy due to position or composition.

• Types of potential energy: chemical, gravitational, electrostatic.

• Law of Conservation of Energy: Energy cannot be created or destroyed, only transformed.

Example: Chemical reactions convert potential energy in bonds to heat.

Units of Energy

Energy is measured in joules (J) or calories (cal).

• 1 cal = 4.184 J

• 1 kJ = 1000 J

Example: The energy required to heat water is often measured in joules.

System, Surroundings, and Closed System

The system is the part of the universe under study; the surroundings are everything else. A closed system can exchange energy but not matter with its surroundings.

• Open system: exchanges both energy and matter.

• Isolated system: exchanges neither energy nor matter.

Example: A reaction in a sealed flask is a closed system.

Heat and Thermal Energy

Heat is energy transferred due to temperature difference. Thermal energy is the total kinetic energy of particles in a substance.

• Heat flows from hot to cold until thermal equilibrium is reached.

• At equilibrium, both objects have the same temperature.

Example: Mixing hot and cold water results in a final temperature between the two.

First Law of Thermodynamics

The first law states that the change in internal energy (ΔE) of a system is equal to the heat (q) added plus the work (w) done on the system.

• Formula: $\Delta E = q + w$

• Includes all forms of energy transfer.

Example: Compressing a gas increases its internal energy.

Stoichiometry Using ΔH

Enthalpy change (ΔH) measures heat flow at constant pressure. It is used to calculate energy changes per mole of reactant.

• Given a reaction: $2\text{H}_2 + \text{O}_2 \rightarrow 2\text{H}_2\text{O}$, $\Delta H = -572\text{ kJ}$

• Means 572 kJ released per 2 moles H2 and 1 mole O2.

• Use conversion factors to find energy for any amount of reactant.

Example: Calculate energy released when 4 g of H2 reacts.

Specific Heat and Heat Capacity

Specific heat (cs) is the amount of heat required to raise the temperature of 1 g of a substance by 1°C. Heat capacity (C) is the amount of heat required to raise the temperature of an object by 1°C.

• Units: cs in J/g·°C; C in J/°C.

• High specific heat means substance heats up slowly; low specific heat means it heats up quickly.

Example: Water has a high specific heat, so it resists temperature changes.

Calculating Heat Transfer

Heat transfer is calculated using mass, specific heat, and temperature change.

• Formula: $q = m c_s \Delta T$

• Alternatively, $q = C \Delta T$ for objects.

Example: Calculate heat needed to raise 100 g of water by 10°C.

Calorimetry

Calorimetry measures heat changes in chemical reactions. Two main types are coffee-cup and bomb calorimetry.

• Coffee-cup calorimeter: Constant pressure; $q = C_{cal} \Delta T + q_{solution}$

• Assume solution has properties similar to water.

• Bomb calorimeter: Rigid container; $\Delta V = 0$, so $q = \Delta E$; $q_{calorimeter} = q_{water} + q_{bomb}$

• If calorimeter includes water, $C_{calorimeter} = C_{calorimeter} + C_{water}$

Example: Measure heat released by combustion in a bomb calorimeter.

Manipulating Thermochemical Equations

Thermochemical equations can be reversed, multiplied, or added to find enthalpy changes for new reactions.

• Reverse reaction: change sign of ΔH.

• Multiply reaction: multiply ΔH by same factor.

• Add reactions: add ΔH values.

Example: Use Hess's Law to find ΔH for a target reaction.

Hess's Law

Hess's Law states that the enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.

• Given several reactions and their ΔH values, rearrange and add to find ΔH for a new reaction.

Example: Calculate ΔH for the formation of CO2 from C and O2 using known reactions.

Table: Comparison of Coffee-Cup and Bomb Calorimetry

Type	Pressure	Measured Quantity	Typical Use
Coffee-cup	Constant (atmospheric)	q (heat at constant pressure)	Solution reactions
Bomb	Constant volume	ΔE (change in internal energy)	Combustion reactions

Additional info: In calorimetry, always check the limiting reactant and adjust calculations for stoichiometry.