The Gibbs phase rule is stated as
Answer: A
Correct answer: \( F = C - P + 2 \)
Degrees of freedom equal components minus phases plus two, the two being temperature and pressure. Every consequence in the subject follows from it: since \( F \) cannot be negative, \( P \le C + 2 \), which is why a one-component system can have at most three phases in equilibrium and no more.
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A phase in the phase rule is a portion of a system that is
Answer: B
A mixture of gases is one phase however many species it contains, because it is homogeneous throughout with no internal boundary. Two immiscible liquids, or several different solids present together, count as one phase each.
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A mixture of nitrogen, oxygen and argon constitutes
Answer: C
Gases mix in all proportions, so the mixture is homogeneous and there is no interface anywhere within it to separate mechanically. The number of components is three but the number of phases is one, and the two counts must never be confused.
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The number of components of a system is the smallest number of independently variable constituents needed to express
Answer: D
For water in all three states one component suffices, since ice, water and steam are all H\( _2 \)O. Where a chemical equilibrium links the species, that relation reduces the count below the number of substances present.
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A degree of freedom is the number of variables that must be fixed to
Answer: A
Correct answer: define the system's condition completely
The degrees of freedom count the intensive variables - temperature, pressure, composition - that may be varied independently without changing the number of phases, and equivalently the number that must be fixed before the state is determined. It says nothing about how equilibrium is reached, only about the equilibrium state.
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A system with zero degrees of freedom is described as
Answer: B
Correct answer: invariant
With \( F = 0 \) nothing can be varied without a phase disappearing, so the state is fixed at a single point on the diagram. The triple point of water is the standard example, and its invariance is exactly why it served as a defining fixed point of the temperature scale.
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For a one-component system existing as a single phase, the number of degrees of freedom is
Answer: C
Correct answer: two
\[ F = 1 - 1 + 2 = 2. \] Both temperature and pressure may be varied independently within a single-phase region, which is why such regions appear as areas on a pressure-temperature diagram rather than as lines or points.
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Along a two-phase curve of a one-component system the degrees of freedom number
Answer: D
Correct answer: one
\[ F = 1 - 2 + 2 = 1. \] Fixing either temperature or pressure fixes the other, which is why two-phase equilibria appear as curves. The vapour pressure of a liquid is a function of temperature alone for precisely this reason.
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The triple point of water is invariant because at that point there coexist
Answer: A
Correct answer: three phases of one component
\[ F = 1 - 3 + 2 = 0. \] Ice, water and vapour coexist at one temperature and one pressure only, 273.16 K and 611 Pa. Nothing can be adjusted without losing a phase, which is what makes the point reproducible enough to define a temperature.
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The fusion curve of water slopes with a negative gradient because ice is
Answer: B
Correct answer: less dense than the liquid
By the Clapeyron equation the slope of the fusion curve is \( dP/dT = \Delta H_{fus}/(T\Delta V) \). Melting absorbs heat, so \( \Delta H \) is positive; but ice contracts on melting, so \( \Delta V \) is negative and the slope is negative. This is why pressure lowers the melting point of ice, almost uniquely among substances.
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