Question

Calculate \(\Delta G^{\circ}\) at \(82^{\circ} \mathrm{C}\) for reactions in which (a) \(\Delta H^{\circ}=293 \mathrm{~kJ} ; \quad \Delta S^{\circ}=-695 \mathrm{~J} / \mathrm{K}\) (b) \(\Delta H^{\circ}=-1137 \mathrm{~kJ} ; \quad \Delta S^{\circ}=0.496 \mathrm{~kJ} / \mathrm{K}\) (c) \(\Delta H^{\circ}=-86.6 \mathrm{~kJ} ; \quad \Delta S^{\circ}=-382 \mathrm{~J} / \mathrm{K}\)

Short answer

Question: Calculate the Gibbs free energy change (ΔG°) for each of the following reactions at 82°C: (a) ΔH° = 293 kJ; ΔS° = -695 J/K (b) ΔH° = -1137 kJ; ΔS° = 0.496 kJ/K (c) ΔH° = -86.6 kJ; ΔS° = -382 J/K Answer: (a) ΔG° = 539.79 kJ (b) ΔG° = -1313.15 kJ (c) ΔG° = 48.87 kJ

Step-by-step solution

Convert the temperature to Kelvin

To convert the given temperature in Celsius to Kelvin, we need to add 273.15: 82°C + 273.15 = 355.15 K.

Convert the entropy to kJ/K

In this reaction, ΔS° is given in J/K. We need to convert it to kJ/K by dividing it by 1000: ΔS° = -695 J/K ÷ 1000 = -0.695 kJ/K.

Calculate ΔG° using the formula

Now we can use the formula ΔG° = ΔH° - TΔS°: ΔG° = 293 kJ - (355.15 K × (-0.695 kJ/K)) = 293 kJ + 246.79 kJ = 539.79 kJ. (b) ΔH° = -1137 kJ; ΔS° = 0.496 kJ/K

Use the temperature in Kelvin

We already have the temperature in Kelvin from part (a): T = 355.15 K.

The entropy is already in kJ/K

In this reaction, ΔS° is given in kJ/K: ΔS° = 0.496 kJ/K.

Calculate ΔG° using the formula

Now we can use the formula ΔG° = ΔH° - TΔS°: ΔG° = -1137 kJ - (355.15 K × 0.496 kJ/K) = -1137 kJ - 176.15 kJ = -1313.15 kJ. (c) ΔH° = -86.6 kJ; ΔS° = -382 J/K

Use the temperature in Kelvin

We already have the temperature in Kelvin from part (a): T = 355.15 K.

Convert the entropy to kJ/K

In this reaction, ΔS° is given in J/K. We need to convert it to kJ/K by dividing it by 1000: ΔS° = -382 J/K ÷ 1000 = -0.382 kJ/K.

Calculate ΔG° using the formula

Now we can use the formula ΔG° = ΔH° - TΔS°: ΔG° = -86.6 kJ - (355.15 K × (-0.382 kJ/K)) = -86.6 kJ + 135.47 kJ = 48.87 kJ.

Key concepts

Chemical Thermodynamics

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. It involves the concepts of internal energy, enthalpy, entropy, and the Gibbs free energy. Each of these quantities plays a vital role in predicting the work that a system can perform and the direction in which a chemical reaction will proceed.

In essence, it provides us with the criterion to predict whether a process will occur spontaneously at constant temperature and pressure. The Gibbs free energy (ΔG), a central concept in chemical thermodynamics, tells us whether a process is thermodynamically favorable. The condition for spontaneity is ΔG < 0. It is calculated using the equation ΔG = ΔH - TΔS, where ΔH represents the change in enthalpy, T is the temperature in Kelvin, and ΔS denotes the change in entropy. Understanding these fundamental concepts is crucial for solving problems related to chemical thermodynamics.

Enthalpy Change

Enthalpy change (ΔH) is a measure of the total heat content of a system and is used to express the amount of energy absorbed or released during a chemical reaction at constant pressure. It is a state function, meaning its value is determined by the state of the system and not the path taken to reach that state.

In reactions where ΔH is positive, the process is endothermic, indicating that the system absorbs heat from the surroundings. Conversely, when ΔH is negative, the process is exothermic, and the system releases heat. The ΔH value is crucial in calculating the Gibbs free energy and plays a significant role in determining whether a reaction will be spontaneous or not.

Entropy Change

Entropy change (ΔS) is a fundamental concept that measures the disorder or randomness of particles within a chemical system. It reflects the number of ways the particles can be arranged while still maintaining the overall structure and environment.

An increase in entropy (ΔS > 0) corresponds to increased disorder, while a decrease in entropy (ΔS < 0) corresponds to increased order. At the microscopic level, processes tend to proceed in the direction that increases the overall entropy of the universe. When it comes to calculating the Gibbs free energy, entropy change is factored into the equation alongside temperature. Thus, understanding entropy is key to predicting the spontaneity and balance of reactions.

Temperature Conversion

Temperature conversion is essential in chemical thermodynamics because equations like the one used for Gibbs free energy require the absolute temperature in Kelvin (K). The Kelvin scale is an absolute, thermodynamic temperature scale and is helpful in scientific calculations.

To convert Celsius to Kelvin, one must add 273.15 to the Celsius temperature. This step is key in many thermodynamic calculations because Celsius and Fahrenheit are relative temperature scales, which are not used in formulas involving absolute quantities such as entropy and enthalpy changes. Therefore, accurately converting temperature into Kelvin ensures the correct application of thermodynamic equations.