Solid ammonium bydrosulphide (NH4 HS) is mixed with arbitrary amounts of gaseous NH3 and H2 S,

Solid ammonium bydrosulphide (NH4 HS) is mixed with...

Solid ammonium bydrosulphide $\left(\mathrm{NH}_{4} \mathrm{HS}\right)$ is mixed with arbitrary amounts of gaseous $\mathrm{NH}_{3}$ and $\mathrm{H}_{2} \mathrm{~S}$, forming a three-constituent system of two phases, undergoing the reaction $$ \mathrm{NH}_{4} \mathrm{HS} \rightleftharpoons \mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{~S} $$ (a) How many components are there, and what is the variance? (b) Assuming that the gaseous phase is a mixture of ideal gases, show that $$ \frac{P \mathrm{NH}_{1} P \mathrm{H}_{4} \mathrm{~s}}{P \mathrm{NH}_{4} \mathrm{HS}}=K $$ (c) If solid $\mathrm{NH}_{4} \mathrm{HS}$ is placed in an evacuated chamber, how many components are there, and what is the variance?

Solid ammonium bydrosulphide $\left(\mathrm{NH}_{4} \mathrm{HS}\right)$ is mixed with arbitrary amounts of gaseous $\mathrm{NH}_{3}$ and $\mathrm{H}_{2} \mathrm{~S}$, forming a three-constituent system of two phases, undergoing the reaction
$$
\mathrm{NH}_{4} \mathrm{HS} \rightleftharpoons \mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{~S}
$$
(a) How many components are there, and what is the variance?
(b) Assuming that the gaseous phase is a mixture of ideal gases, show that
$$
\frac{P \mathrm{NH}_{1} P \mathrm{H}_{4} \mathrm{~s}}{P \mathrm{NH}_{4} \mathrm{HS}}=K
$$
(c) If solid $\mathrm{NH}_{4} \mathrm{HS}$ is placed in an evacuated chamber, how many components are there, and what is the variance?

Key Concepts

Heterogeneous Equilibria

Heterogeneous equilibria involve reactants and products in different phases, such as mixtures of gases and solids. In these systems, the activities of pure phases like solids are constant, usually taken as one, meaning that only the components in the gas phase or the solution phase need to be accounted for in the equilibrium expressions. This simplification is crucial for correctly applying the equilibrium constant expression and for the analysis of such systems using methods like the Gibbs phase rule.

Ideal Gas Behavior

Ideal gas behavior describes the state of a gas wherein the particles are assumed to have negligible interactions and occupy no volume relative to the container. This assumption allows the use of simplified relationships like the ideal gas law (PV = nRT), which is particularly useful in calculating partial pressures in mixtures. In equilibrium expressions involving gases, the ideal gas approximation simplifies the derivation and interpretation of the equilibrium constant in terms of partial pressures, making it easier to predict the system’s response to changes in conditions.

Gibbs Phase Rule

The Gibbs phase rule is a fundamental principle in thermodynamics that determines the number of degrees of freedom (variance) in a thermodynamic system, which is given by the formula F = C - P + 2, where C represents the number of independent components and P represents the number of phases present. In systems where chemical reactions occur or in heterogeneous equilibria where pure solids or liquids may be involved, the identification of independent components must take into account the constraints imposed by these reactions or phases. This rule is critical for understanding how many variables (such as temperature, pressure, or concentration) can be independently changed without disturbing the equilibrium state.

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in constant concentrations of the reactants and products. This concept is central to predicting the outcome of reactions under various conditions, and in heterogeneous systems, equilibrium expressions must consider only the species whose activities change; for example, the activities of pure solids are constant and usually taken as unity. Equilibrium constants provide a quantitative measure of the position of the equilibrium and are essential for relating partial pressures or concentrations in reacting systems.

Transcript

00:01 In this problem, we need to answer various questions regarding the equilibrium of this reaction.

00:07 We can begin by starting to fill in a reaction table since we are given an initial amount of solid that we have.

00:14 We are told that we have 6 .1589 grams of nh4hs.

00:27 And if we convert this into an initial amount of moles, we know that a smaller mass from the periodic.

00:34 Table we can calculate to be 51 .11 grams per mole.

00:41 And so we initially have about 0 .1205 moles of nh4hs.

00:52 So we can fill that initial number of moles in to our reaction table for the solid.

01:01 So again that was 0 .1205 moles.

01:07 We initially do not have any of the gaseous products.

01:10 The changes will be minus x, plus x, and plus x.

01:20 And in part a, we want to determine what the value of kp is if we are told what the total equilibrium pressure is.

01:34 So we know that at equilibrium, the total pressure is equal to 0 .709 atmospheres.

01:44 And we know that in any case the total pressure will be the sum of the partial pressures of all the gases.

01:54 So it would be the equilibrium partial pressure of nh3 plus the equilibrium partial pressure of h2s.

02:08 We need to solve for both of those equilibrium partial pressures so that we can plug them into the equilibrium expression for kp in order to find kp.

02:17 Based on the reaction table, we know that once we are at equilibrium, then the total partial pressure of both nh3 and h2s will both be equal to one another, and that change will be equal to x.

02:37 And whatever that change is, that will subtract from the initial amount of the solid that we have, and that amount will decompose.

02:48 And so because we know that equilibrium pnh3 is equal to ph2s we can set those equal to one another and say that this is equal to two times a partial pressure of nh3 or two times a partial pressure of h2s since they are equal so all we have to do to isolate pnh3 is divide 0 .709 by 2 when we do that we find that the equilibrium partial pressure of nh3 is equal to the equilibrium partial pressure of h2s, which is equal to 0 .355 atmospheres.

03:36 And now we can form the equilibrium expression for kp.

03:41 These are the only gases, so this would be the equilibrium partial pressure of nh3 times the equilibrium partial pressure of h2s.

03:50 But both of these are equal to this value, so we should just square that value, in order to determine kp.

03:58 When we do that, we will find that kp comes out to about 0 .126.

04:11 And now in part b, we need to determine the percentage of that initial amount of solid that has decomposed once we get to equilibrium...

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