Pharmaceutical Polymorphism Quiz

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Questions and Answers

What does the term $a_i$ represent in the context of free energy changes?

Equilibrium constant for component i

Concentration of component i

Activity of component i (correct)

Standard free energy of component i

What is the relationship between activity and concentration?

Activity is directly proportional to concentration with a coefficient. (correct)

Activity and concentration are independent variables.

Activity is equal to concentration without any coefficients.

Activity is inversely proportional to concentration.

What is the purpose of using the activity coefficient ($eta_i$) in thermodynamics?

To express equilibrium constants solely in terms of concentrations.

To simplify calculations involving concentrations.

To convert activities into molar concentrations.

To account for deviations from ideal behavior in real systems. (correct)

Under what conditions can concentrations be used as an approximation for activities?

Depending on the specific context of usage. Signup and view all the answers

Which of the following equations represents the relationship between free energy change ($ riangle G$) and the equilibrium constant ($K$)?

$ riangle G = riangle G^{ullet} + RT ln(K)$ Signup and view all the answers

What is the significance of the equilibrium constant ($K$) in terms of activities?

It relates the activities of products to reactants at equilibrium. Signup and view all the answers

In the equation $a_i = eta_i[i]$, what does $eta_i$ represent?

The activity coefficient of component i Signup and view all the answers

Which component in the equation $ riangle G = riangle G^{ullet} + RT ln(K)$ reflects standard conditions?

$ riangle G^{ullet}$ Signup and view all the answers

How does the activity of a component in a real system differ from that in an ideal system?

It reflects interactions between particles that are not ideal. Signup and view all the answers

What determines the stability of different crystalline polymorphs of a pharmaceutical compound?

Temperature and pressure conditions Signup and view all the answers

In a system consisting of three components A, B, and C, how is the total free energy expressed for a real system?

GT,P = μA nA + μB nB + μC nC Signup and view all the answers

Which phase diagram feature indicates the presence of two distinct solid forms in a compound?

Two solid regions, S1 and S2 Signup and view all the answers

What is the significance of chemical potential in a real system?

It indicates the contribution of each component to overall free energy. Signup and view all the answers

What is the correct relationship for free energy changes in non-equilibrium systems?

ΔG - ΔG° = RTlnKeq Signup and view all the answers

What is one implication of crystal polymorphism in pharmaceuticals?

Different forms may have varying bioavailability Signup and view all the answers

How does the existence of non-ideal systems affect the definition of free energy?

Real systems require adjustments to theoretical free energy definitions. Signup and view all the answers

Which statement accurately describes the role of temperature in crystal polymorphism?

Lower temperatures favor the most stable polymorph. Signup and view all the answers

What does the phase diagram convey regarding the conditions of two polymorphs?

It demonstrates the variation of stability with specified conditions. Signup and view all the answers

What does the change in free energy equation ΔG = −RTlnKeq imply in an equilibrium context?

It connects free energy to the ratio of reactants to products at equilibrium. Signup and view all the answers

Study Notes

Polymorphism

Many pharmaceutical compounds exist in multiple crystalline forms known as polymorphs.
Paracetamol, for example, has at least three polymorphs.
The stability of these polymorphs can vary with temperature.
Amorphous (non-crystalline) solid forms are also possible.
Controlling the crystal form of a drug product is crucial as it affects solubility and other properties.

Phase Diagrams

Phase diagrams can be used to represent the stability of different polymorphs under varying temperatures and pressures.
Each polymorph is represented by a distinct solid region (S1, S2, etc.) in the diagram.
The most stable polymorph, or the one preferred under specific conditions, is indicated by the corresponding region on the diagram.

Chemical Potential

In ideal systems, total free energy (G) is the sum of the free energies of individual components (GA + GB + GC).
In real systems, interactions between components affect the total free energy.
The contribution of each component to the total free energy is represented by its chemical potential (𝜇).
Chemical potential reflects the change in free energy resulting from an addition or removal of that component.

Free Energy Changes in Real Systems

For a system at equilibrium, the change in free energy (∆G°) is related to the equilibrium constant (Keq) by the equation: ∆G° = −RTlnKeq.
For a system not at equilibrium, the change in free energy (∆G) is related to ∆G° and Keq by the equation: ∆G − ∆G° = RTlnKeq.
The free energy change in an ideal gas can be represented by the equation: G = G° + RTln(P/P°).
For a real system (e.g., a solution), the chemical potential (𝜇i) of component 'i' is related to its standard chemical potential (𝜇i°), temperature (T), and activity (ai) by the equation: 𝜇𝑖 = 𝜇𝑖° + 𝑅𝑇 ln 𝑎𝑖.
Activity (ai) is proportional to concentration ([i]) and related by the activity coefficient (γ) and the equation: ai = γi[i].
For a process like A + B ⇌ C + D, the change in free energy (∆G) can be represented as: ∆𝐺 = ∆𝐺 ° + 𝑅𝑇 ln 𝐾.
The equilibrium constant (K) for the process is given by: 𝐾= 𝑎𝐶𝑐 𝑎𝐷𝑑 / (𝑎𝐴 𝑎𝐵).
Activities can be replaced by concentrations as an approximation in many cases.

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Description

Test your knowledge on pharmaceutical polymorphism and its importance in drug stability. Explore concepts such as phase diagrams and chemical potential, which play critical roles in determining the properties of different crystalline forms of compounds. Understand why controlling crystal forms is vital in the pharmaceutical industry.