Quiz 7

Thermochemistry and Calorimetry

Thermodynamics of Gases

Thermodynamics is the study of energy changes, particularly heat and work, in chemical systems. The behavior of ideal gases under changing conditions is a fundamental topic in general chemistry.

• Ideal Gas Law: Relates pressure, volume, temperature, and amount of gas: $PV = nRT$

• Work Done by a Gas: When a gas expands against a constant external pressure, the work is given by $w = -P_{ext} imes riangle V$

• Internal Energy Change ($riangle U$): For an ideal gas, $riangle U = nC_v riangle T$ where $C_v$ is the molar heat capacity at constant volume.

• Heat ($q$): The heat absorbed or released at constant volume is $q = nC_v riangle T$

• First Law of Thermodynamics: $\triangle U = q + w$

• Example: Calculating $q$, $w$, and $\triangle U$ for a piston containing two moles of an ideal gas expanding against a constant pressure, with a temperature change from 25°C to 50°C.

Calorimetry and Specific Heat

Calorimetry is the measurement of heat changes in physical and chemical processes. The specific heat capacity is a property that quantifies the amount of heat required to change the temperature of a substance.

• Specific Heat Capacity ($c$): The amount of heat required to raise the temperature of 1 gram of a substance by 1 K (or 1°C).

• Heat Transfer Equation: $q = mc\triangle T$ where $m$ is mass, $c$ is specific heat, and $\triangle T$ is temperature change.

• Example: A hot metal is placed in water, and the final equilibrium temperature is measured. The specific heat capacity of the metal can be calculated using the heat gained by water and lost by the metal.

• Application: Determining the specific heat of a metal using calorimetry, with water as the calorimeter medium.

Enthalpy Changes in Chemical Reactions

Enthalpy ($H$) is a thermodynamic quantity that represents the heat content of a system at constant pressure. The change in enthalpy ($\triangle H$) during a reaction is a key concept in thermochemistry.

• Standard Enthalpy Change ($\triangle H^\circ$): The enthalpy change when reactants and products are in their standard states.

• Hess's Law: The total enthalpy change for a reaction is the sum of the enthalpy changes for individual steps.

• Example: Calculating $\triangle H$ for the dissolution of cesium sulfate in water using given enthalpy values for reactants and products.

• Equation: $\triangle H_{rxn} = \sum \triangle H_{f,products} - \sum \triangle H_{f,reactants}$

Application of Hess's Law

Hess's Law allows the calculation of enthalpy changes for reactions that are difficult to measure directly by combining known enthalpy changes of related reactions.

• Procedure:

  1. Write the target reaction.

  2. Arrange given reactions so that their sum yields the target reaction.

  3. Add or subtract their enthalpy changes accordingly.

• Example: Using Hess's Law to determine $\triangle H$ for $\mathrm{N}_2(g) + \mathrm{Cl}_2(g) \rightarrow 2\mathrm{NCl}(g)$ from given reactions and enthalpy changes.

Calorimetry with Solutions

When a salt or compound dissolves in water, the temperature change can be used to calculate the enthalpy of dissolution using calorimetry.

• Heat of Solution ($\triangle H_{sol}$): The enthalpy change when a solute dissolves in a solvent.

• Equation: $q = mc\triangle T$ (for the solution, assuming negligible heat capacity of the calorimeter)

• Example: Dissolving ammonium perchlorate ($\mathrm{NH}_4\mathrm{ClO}_4$) in water and measuring the temperature change to calculate $\triangle H_{sol}$.

Sample Table: Standard Enthalpy Values (Inferred from Questions)

The following table summarizes standard enthalpy values used in calculations:

Substance	Standard Enthalpy of Formation ($\triangle H_f^\circ$) (kJ/mol)
Cs$_2$SO$_4$(s)	-1443.0
Cs$^+$(aq)	-285.8
SO$_4^{2-}$(aq)	-909.3
NH$_4$ClO$_4$(s)	Not provided
NH$_4^+$(aq)	Not provided
ClO$_4^-$(aq)	Not provided
NO(g)	90.3
NCl(g)	38.6

Additional info: Some enthalpy values are inferred from the context of the questions and may not be complete.

Key Equations Summary

• $PV = nRT$

• $w = -P_{ext} \triangle V$

• $q = mc\triangle T$

• $\triangle U = q + w$

• $\triangle H_{rxn} = \sum \triangle H_{f,products} - \sum \triangle H_{f,reactants}$