From data in Appendix 4, calculate ΔH^∘, ΔS^∘, and ΔG^∘ for each of the following reactions at 2

From data in Appendix 4, calculate ΔH^∘, ΔS^∘, and ΔG^∘ for...

From data in Appendix $4,$ calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for each of the following reactions at $25^{\circ} \mathrm{C} .$ a. $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ b. $6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g)$ c. $\mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{H}_{3} \mathrm{PO}_{4}(s)$ d. $\mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$

From data in Appendix $4,$ calculate $\Delta H^{\circ}, \Delta S^{\circ},$ and $\Delta G^{\circ}$ for
each of the following reactions at $25^{\circ} \mathrm{C} .$
a. $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
b. $6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g)$
c. $\mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{H}_{3} \mathrm{PO}_{4}(s)$
d. $\mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$

Key Concepts

Standard Enthalpy Change (?H°)

This concept represents the overall heat absorbed or released during a chemical reaction carried out under standard conditions. It is calculated by taking the sum of the standard enthalpies of formation of the products, each multiplied by its stoichiometric coefficient, and subtracting the sum of the standard enthalpies of formation of the reactants. ?H° indicates whether a reaction is endothermic (heat-absorbing) or exothermic (heat-releasing), which is essential for understanding energy changes in chemical processes.

Standard Entropy Change (?S°)

Standard entropy change is a thermodynamic quantity that measures the change in disorder or randomness as a system undergoes a chemical reaction under standard conditions. It is calculated by summing the standard molar entropies of the products (weighted by their stoichiometric coefficients) and subtracting the corresponding sum for the reactants. This concept helps predict the degree of molecular randomness and plays a critical role in determining the spontaneity of a reaction.

Standard Gibbs Free Energy Change (?G°)

This thermodynamic function combines both enthalpy and entropy changes to determine the overall spontaneity of a reaction at constant temperature and pressure. ?G° is calculated using the equation ?G° = ?H° - T?S°, where T is the temperature in Kelvin. A negative ?G° indicates a spontaneous reaction under standard conditions, while a positive value signifies non-spontaneity, making this concept central to predicting reaction behavior.

Use of Standard Thermodynamic Data and Hess's Law

Calculations of ?H°, ?S°, and ?G° for reactions typically rely on tabulated standard thermodynamic data such as standard enthalpies of formation and standard molar entropies. Hess's Law underpins these calculations by stating that the total enthalpy change for a reaction is the same, regardless of the pathway taken, allowing the use of formation data to compute reaction enthalpies. This approach is fundamental in thermochemistry for quantifying energy changes and assessing reaction feasibility.

Transcript

00:01 For all the calculations in this problem, we're going to use the standard state, delta g of formation, delta h of formation, and then the absolute entropy value for all reactants and products that are found in these chemical reactions.

00:20 What we do is we look up the values i just discussed, standard delta g's of formation, delta h is of formation, and absolute standard entropyes.

00:29 And we take those values for the products multiplied by their coefficients and subtract off those values for the reactants multiplied by their coefficients.

00:46 And this is how we determine the change in entropy, enthalpy, and gives free energy for the entire reactions.

00:56 For the first chemical reaction, this one here, we will look up the delta h, delta g, and s values for carbon dioxide first, multiplied by its coefficient of 1.

01:15 Delta h of formation for carbon dioxide is negative 393 .5, delta g of formation is negative 394, and absolute s is 214.

01:25 We'll then do it for water, two times the delta h of formation of water.

01:30 In standard state, 242, and then delta g, and then s, and then we'll subtract off 1 times the delta h of formation of methane gas, negative 75, delta g of formation of methane gas, negative 51, and entropy of methane gas 186.

01:51 And then last of all, for oxygen, 2 times, delta h of formation, which is 0, delta g of formation is zero for oxygen and entropy is 205 and then we sum everything up so the delta h standard for this entire reaction is negative 202 .5 kilojoules delta g standard for this reaction is negative 801 kilojoules and delta s standard for this reaction is negative 4 joules per kelvin remember all these values in the back of the book are in kilojoules for delta h and delta g, but they're in units of joules per kelvin for s.

02:38 Now we'll move on to the next reaction.

02:41 6 moles carbon dioxide reacts with 6 moles liquid water, producing 1 mole of glucose, and 6 moles of oxygen.

02:53 Again, we'll go to the back of the book.

02:57 1 mole, multiplied by the delta h of formation of glucose, negative 127, delta g of formation of glucose, negative 1 .27, delta g of formation of glucose, negative 9, 11 and 1 times the absolute s of glucose as a solid 212 joules per kelvin.

03:14 We'll then do the same thing for oxygen and then subtract off six times the delta h of formation of carbon dioxide negative 393 .5, 6 times the delta g of formation of carbon dioxide negative 394 and then six times the entropy of carbon dioxide 214 jules per kelvin.

03:35 And then last of all for liquid water.

03:39 6 times the delta h of formation, 6 times the delta g of formation, and 6 times the entropy...

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