A metal salt with the formula MCl2 crystallizes from water to form a solid with the composition

A metal salt with the formula MCl2 crystallizes from water...

A metal salt with the formula $\mathrm{MCl}_{2}$ crystallizes from water to form a solid with the composition $\mathrm{MCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}$. The equilibrium vapor pressure of water above this solid at $298 \mathrm{~K}$ is $18.3 \mathrm{mmHg}$. What is the value of $\Delta G$ for the reaction $\mathrm{MCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}(s) \rightleftharpoons \mathrm{MCl}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(g)$ when the pressure of water vapor is $18.3 \mathrm{mmHg} ?$ When the pressure of water vapor is $760 \mathrm{mmHg}$ ?

Key Concepts

Vapor Pressure and Its Role in Phase Equilibria

Vapor pressure is the pressure exerted by a vapor above its liquid or solid phase when the two are in equilibrium. It is a pivotal concept in phase equilibria, as it determines the tendency of a substance to evaporate or condense. In the problem context, the equilibrium vapor pressure of water from a hydrated salt informs the extent of dehydration when the system is perturbed from equilibrium, affecting the reaction quotient and thereby the ?G of the process.

Standard States and Non-Standard Conditions

Standard states refer to a set of conditions (typically 1 bar for gases and 1 M for solutes) under which thermodynamic properties are defined; deviations from these conditions require adjustments using the RT ln Q term in the Gibbs free energy expression. When a reaction is not at standard conditions, the actual free energy change must account for the difference in the chemical potential of the reactants and products, illustrated by the pressure or concentration dependence in Q.

Gibbs Free Energy Change

Gibbs free energy change (?G) is a thermodynamic function that indicates the spontaneity of a chemical reaction at constant temperature and pressure. It is calculated using the relationship ?G = ?G° + RT ln Q, where ?G° is the standard free energy change, R is the gas constant, T is the temperature in Kelvin, and Q is the reaction quotient. A negative ?G indicates that the reaction is spontaneous under the given conditions, while a positive value means it is non-spontaneous.

Reaction Quotient (Q) and Its Role in Equilibrium

The reaction quotient (Q) is a measure of the relative amounts of products and reactants present during a reaction, and is used to determine the direction in which a reaction must shift to reach equilibrium. For reactions involving gases, Q is expressed in terms of partial pressures or fugacities of the gaseous components. In the context of the problem, Q is directly related to the pressure of water vapor, influencing the non-standard ?G via the RT ln Q term in the Gibbs free energy equation.

Transcript

00:01 In this question, we've been given a reaction and we've been asked to determine the gibbs energy change.

00:07 And what is important about the gibbs energy change? it is a state parameter that helps us identify the spontaneity of a reaction.

00:18 So whenever our gibbs energy is less than zero, it tells us that reaction is spontaneous.

00:23 But when it is greater than zero, it tells us that reaction is not spontaneous.

00:28 In other words, it will not okay on its own without an, external force or a source of energy so moving on we know that the delta g delta g is equal to the standard gives energy change plus r t lin q p and this is just an equilibrium constant and we know that at equilibrium our q p is going to be equal to our kp and we also know that this standard gives energy the standard gives energy is given by negative r lind kp so if at equilibrium q p is equal to kp what we have here is delta g being equal to negative r t lin kp plus r tlin instead of qp we now have kp so at the end of the day this is delta g is equal to zero kilo chowls per more and then moving forward we want to determine we are still using the same formula delta g is equal to the standard plus r t lin qp so what we have here this is equal to negative rt lin kp plus rt lin qp so if we just factor out this common factor what we have is delta g being equal to r t lin qp over kp and for us to determine first of all we have to determine the kp we also have to determine the kp we also have to determine the the qp.

02:28 So coming to determining kp, we know that kp is equal to p, the partial pressure of the gas.

02:37 Those are that the reactions are not gases, so they won't be part of the kp expression.

02:41 And remember, we have to raise this to the power of this dichometric coefficient of water, which is squared...

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