Question

Calculate \(\Delta G^{\circ}\) for the following reactions at \(25^{\circ} \mathrm{C}\) : (a) \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\) (b) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (c) \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\) See Appendix 2 for thermodynamic data.

Short answer

\(\Delta G^{\circ}\) for the first reaction is -1139.2 kJ, for the second reaction is -140 kJ, and for the third reaction is -2712.2 kJ.

Step-by-step solution

Consider the first reaction

The given reaction is: \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s)\). According to the table in Appendix 2, the standard free energy of formation, \(\Delta G^{\circ}\), for \(\mathrm{MgO}(s)\) is -569.6 kJ. So, \(\Delta G^{\circ}\) for this reaction would be \(2 * (-569.6 kJ) - [2 * 0 + 0] = -1139.2 kJ\).

Consider the second reaction

The given reaction is: \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\). From Appendix 2, you get that \(\Delta G^{\circ}\) of \(\mathrm{SO}_{2}(g)\) and \(\mathrm{SO}_{3}(g)\) are -300.4 kJ and -370.4 kJ respectively. The \(\Delta G^{\circ}\) for this reaction would be \(2 * (-370.4 kJ) - [2 * (-300.4 kJ) + 0] = -140 kJ\).

Consider the third reaction

The given reaction is: \(2 \mathrm{C}_{2} \mathrm{H}_{6}(g)+7 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l)\). From Appendix 2, you can find the \(\Delta G^{\circ}\) of \(\mathrm{C}_{2} \mathrm{H}_{6}(g)\), \(\mathrm{CO}_{2}(g)\), \(\mathrm{H}_{2} \mathrm{O}(l)\), which are -32.8 kJ, -394.4 kJ, and -237.1 kJ respectively. So, the calculation yields: \(4 * (-394.4 kJ) + 6 * (-237.1 kJ) - [2 * (-32.8 kJ) + 7 * 0] = -2712.2 kJ\).

Key concepts

Thermodynamics

Thermodynamics is a fundamental physics concept that studies energy and its transformations. In the realm of chemistry, it primarily deals with how energy is transferred during chemical reactions. A key focus is on the changes in enthalpy, entropy, and free energy. These changes help to predict whether a reaction will occur spontaneously under a given set of conditions.

For chemical reactions, understanding thermodynamics involves:

• Enthalpy ( Delta H a measure of heat released or absorbed in a reaction).
• Entropy ( Delta S a measure of the disorder or randomness in a system).
• Gibbs Free Energy ( Delta G a measure of the maximum reversible work a system can do).

The Gibbs Free Energy equation combines both enthalpy and entropy: Delta G = Delta H - T Delta S , where T is the temperature in Kelvin.

When Delta G is negative, a reaction is considered spontaneous, while a positive value suggests it is non-spontaneous. Zero means the system is at equilibrium. This understanding is crucial in predicting reaction behavior, designing processes, and even in industries for efficient energy use.

Chemical Reactions

Chemical reactions are processes where substances are transformed into different substances. They involve the breaking and forming of bonds, which leads to energy changes in the system. Energy changes often determine whether the reactions proceed spontaneously or if an additional input of energy is needed. Analyzing these reactions requires a clear understanding of reactants, products, and the possible pathways that might lead to the desired end-products.

Let's check the role of Delta G in chemical reactions:

• If Delta G is negative, the reaction releases free energy and proceeds spontaneously.
• If Delta G is positive, the reaction requires energy input to proceed.
• If Delta G is zero, the system is at equilibrium.

For the examples given in the exercise:

• The reaction of magnesium ( u Mg(s)) with oxygen ( u O_{2}(g)) forms magnesium oxide ( u MgO(s)), releasing significant energy, indicating spontaneity.
• Sulfur dioxide ( u SO_{2}(g)) reacting with oxygen ( u O_{2}(g)) to form sulfur trioxide ( u SO_{3}(g)) also releases energy, vital for processes like pollution control and acid rain formation.
• Combustion of ethane ( u C_{2}H_{6}(g)) is highly exergonic, vital in energy production as it releases energy stored in hydrocarbons.

Standard Free Energy of Formation

The standard free energy of formation ( Delta G^{ u}) refers to the change in Gibbs Free Energy when one mole of a compound is formed from its elements in their standard states (pure, most stable form at 1 atm pressure and 298.15 K temperature). This measure is crucial in understanding the stability of compounds and forming reactions.

In reactions, standard free energy helps in:

• Calculating overall Delta G by combining the energies from reactants and products.
• Predicting reaction feasibilities and calculating unknown values when some of the data is unavailable.
• Evaluating the environmental and economic viability of chemical processes based on energy efficiency.

For the exercises, these values from Appendix 2 were used to compute the Delta G for each reaction, predicting their spontaneity and driving conditions under standard state conditions. By understanding standard free energy of formation, one can not only gauge the behavior of reactions but also optimize them for desired outcomes in both laboratory and industrial settings.