Problem 60 - Chemistry: The Central Science in SI Units, Global Edition

Question

Using data from Appendix \(\mathrm{C}\), calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)\) (b) \(\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)\) (d) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

(a) ∆G = -109.8 kJ/mol, spontaneous (b) ∆G = -3298.7 kJ/mol, spontaneous (c) ∆G = -3189.1 kJ/mol, spontaneous (d) ∆G = -196.6 kJ/mol, spontaneous

Step 1: Obtain Gibbs free energy values from Appendix C

Reference the values of Gibbs free energy (G) for Ag(s), Cl₂(g), and AgCl(s).

Step 2: Use the equation to calculate ∆G for the reaction

Calculate the change in Gibbs free energy (∆G) using the equation: ∆G = ∆G(products) - ∆G(reactants) ∆G = [2 × G(AgCl)] - [2 × G(Ag) + G(Cl₂)] Calculate the value of ∆G and determine whether the reaction is spontaneous at 298 K. (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ Repeat the steps from the first reaction. (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ Repeat the steps from the first reaction. (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$ Repeat the steps from the first reaction. For each reaction, if the calculated ∆G is negative, the reaction is spontaneous at 298 K under standard conditions.

Key Concepts

Thermodynamics

Thermodynamics is a branch of physics that studies how energy changes in a system. In your textbook exercise, we are dealing with Gibbs Free Energy, a concept within thermodynamics. It helps predict whether a chemical reaction will release energy or require energy to proceed.

Thermodynamics breaks down into several laws, but the most relevant for us is the second law. It states that systems naturally progress towards a state of maximum entropy, or disorder, unless energy is added to the system. This is where Gibbs Free Energy becomes useful. It combines enthalpy (heat content) and entropy (disorder) to determine a reaction's spontaneity under constant temperature and pressure.

To calculate Gibbs Free Energy (abla G), you use the equation: \[abla G = abla H - Tabla S\] where \(abla H\) is the change in enthalpy, \(T\) is the temperature in Kelvin, and \(abla S\) is the change in entropy. By calculating \(abla G\), we can determine if a reaction happens spontaneously or needs external energy.

Chemical Reactions

In the context of your exercis…drawer, chemical reactions involve transforming reactants into products. These reactions can either absorb or release energy.

Your task often involves calculating the change in Gibbs Free Energy (abla G) to assess if these reactions are spontaneous. For example, the chemical reaction \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{AgCl}(s)\) shows how silver and chlorine react to form silver chloride. In this process:

• Reactants: Silver metal and chlorine gas.
• Product: Silver chloride, a solid compound.

We calculate \(abla G\) by subtracting the Gibbs energy values of the reactants from the products.

This value helps in predicting whether a chemical reaction will proceed under given conditions. A negative \(abla G\) means the reaction can occur naturally without needing additional energy, whereas a positive value requires external energy input.

Spontaneity

A reaction is considered spontaneous if it occurs naturally without any additional energy input. Spontaneity does not imply a reaction will occur quickly but rather that it is thermodynamically favorable.

In terms of Gibbs Free Energy, spontaneity is directly connected to the sign of \(abla G\). Here's how to interpret it:

• If \(abla G < 0\), the reaction is spontaneous. It means the system releases energy, often making the surroundings warmer.
• If \(abla G > 0\), the reaction is non-spontaneous. Therefore, you'll need to provide energy to the system to make the reaction happen.
• If \(abla G = 0\), the system is at equilibrium. No net change occurs without external influence.

For example, in the reaction \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)\), computing \(abla G\) allows us to determine whether hydrogen peroxide will naturally decompose into water and oxygen under standard conditions.

Standard Conditions

When discussing Gibbs Free Energy, it's crucial to understand standard conditions. These are a set of agreed-upon conditions used to simplify calculations and provide consistency for experiments and discussions in chemistry.

Standard conditions generally mean:

• Temperature is at 298 K, or 25°C.
• Pressure is at 1 bar or approximately 1 atmosphere.
• Concentration is 1 molar for solutions.

Using these standard conditions allows chemists to predict and compare the Gibbs Free Energy changes across different reactions universally. It's important because these conditions are assumed for calculating Gibbs Free Energy tables found in appendices, such as Appendix C.

In our calculations, like the one you performed for \(\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \rightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)\), assumptions about standard conditions allow for more straightforward and consistent analysis in determining if a reaction is spontaneous.