Consider this reaction occurring at 298 K : BaCO3(s) ⇌BaO(s)+CO2(g) a. Show that the reaction i

Consider this reaction occurring at 298 K : BaCO3(s)...

Consider this reaction occurring at $298 \mathrm{~K}$ : $$\mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)$$ a. Show that the reaction is not spontaneous under standard conditions by calculating $\Delta G_{\mathrm{rxn}}^{\circ}$. b. If $\mathrm{BaCO}_{3}$ is placed in an evacuated flask, what is the partial pressure of $\mathrm{CO}_{2}$ when the reaction reaches equilibrium? c. Can the reaction be made more spontaneous by an increase or decrease in temperature? If so, at what temperature is the partial pressure of carbon dioxide $1.0 \mathrm{~atm}$ ?

Consider this reaction occurring at $298 \mathrm{~K}$ :
$$\mathrm{BaCO}_{3}(s) \rightleftharpoons \mathrm{BaO}(s)+\mathrm{CO}_{2}(g)$$
a. Show that the reaction is not spontaneous under standard conditions by calculating $\Delta G_{\mathrm{rxn}}^{\circ}$.
b. If $\mathrm{BaCO}_{3}$ is placed in an evacuated flask, what is the partial pressure of $\mathrm{CO}_{2}$ when the reaction reaches equilibrium?
c. Can the reaction be made more spontaneous by an increase or decrease in temperature? If so, at what temperature is the partial pressure of carbon dioxide $1.0 \mathrm{~atm}$ ?

Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is a thermodynamic quantity that indicates whether a reaction is spontaneous or non-spontaneous under given conditions. A negative ?G represents a reaction that can occur spontaneously, while a positive ?G indicates that the reaction is non-spontaneous without external intervention. Calculating ?G under standard conditions is a common method to predict the direction of the reaction and assess its feasibility.

Standard Reaction Conditions

Standard reaction conditions refer to a set of defined parameters (typically 1 atm for gases, 1 M concentration for solutions, and a specified temperature, such as 298 K) under which thermodynamic data are measured and reported. Using these standard states allows for the consistent calculation and comparison of reaction properties like ?G° (standard Gibbs free energy change).

Chemical Equilibrium

Chemical equilibrium is the state in which the rates of the forward and reverse reactions are equal, resulting in constant concentrations or partial pressures of the reactants and products. In heterogeneous reactions, where different phases are involved, only the species in the gas or solution phase typically contribute to the equilibrium constant expression. Equilibrium concepts help in relating partial pressures of gaseous products to the equilibrium constant.

Temperature Dependence of Equilibrium

The effect of temperature on equilibrium is governed by the interrelationship between thermodynamic quantities such as enthalpy, entropy, and Gibbs free energy. According to Le Châtelier’s Principle, changing the temperature can shift the position of equilibrium, favoring either the forward or reverse reaction. Adjusting the temperature can thus be used to make a non-spontaneous reaction more spontaneous, and calculations involving the temperature dependence of ?G can determine conditions at which specific equilibrium states, such as a desired partial pressure, are achieved.

Transcript

00:01 So this is a multi -step problem, and the first part of this problem is wanting to show that delta g, this reaction is non -spontaneous.

00:11 So the reaction is barium carbonate, v .a .c .03 as a solid, going to barium oxide, which is also a solid, and also making co2 gas.

00:29 And so you can calculate this using the formula listed below where delta g of your reaction.

00:35 Is the gives free energy of your product minus gives free energy of your reactants, accounting for the moles of your products and reactants.

00:45 For this problem, all the moles are one, so you can just ignore the ends.

00:52 And so now we just plug in numbers that we can find in our appendix of our textbook, which i've included up here.

00:58 And so we have delta g not equals your products minus reactants.

01:04 So let's add up the products.

01:07 So for barium oxide, you have minus 520 .3 plus negative 394 .4 minus your reactant, so minus negative 1134 .4 for your barium carbonate.

01:30 And so this comes out to be 219 .7 kilojoules per mole.

01:42 And so that's the first part of this problem.

01:45 And since this number is positive, this reaction is not.

01:47 Spontaneous.

01:50 Next part of this problem is trying to figure out what the partial pressure would be at equilibrium under non -standard state conditions.

01:57 So the equation we use for this part is delta g equals delta g not...

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