The Clausius-Clapeyron equation is obtained from the Clapeyron equation by assuming that
Answer: C
Those two approximations replace the volume change with the ideal gas volume and give the familiar logarithmic form. They are good well below the critical point and poor as it is approached. Near the critical point the liquid volume is no longer small.
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All of the following are assumptions behind the Clausius-Clapeyron equation EXCEPT
Answer: D
Pressure varies along a vapour pressure curve by definition, so constancy would be self-contradictory. The other three are the standard simplifications that produce the logarithmic form. Each may be relaxed at the cost of a more awkward integral.
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State whether the following is true or false.
A plot of the logarithm of vapour pressure against reciprocal absolute temperature is nearly a straight line.
Answer: A
That linearity is the direct consequence of the Clausius-Clapeyron equation with constant latent heat, and its slope gives the enthalpy of vaporisation. Slight curvature reflects the temperature dependence of the latent heat.
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The Antoine equation differs from Clausius-Clapeyron in that it
Answer: B
The extra constant is a purely empirical correction that greatly improves the fit over a moderate range. Its parameters are tabulated and are valid only over the range for which they were regressed. Extrapolating beyond that range can be badly wrong.
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A residual property is defined as the difference between
Answer: C
Splitting a property this way lets the easy ideal gas part come from heat capacity data and the correction come from an equation of state. Residual and excess properties are different ideas and are frequently confused.
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Three of the following are Maxwell relations in some form. Which is the odd one out?
Answer: D
The ideal gas law is an equation of state describing a particular idealised substance, while the other three are identities that hold for every substance. Confusing the two categories leads to relations being applied where they do not hold.
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Consider the following statements about residual and excess properties.
1. A residual property measures departure from ideal gas behaviour.
2. An excess property measures departure from ideal solution behaviour.
3. The two terms mean the same thing.
Answer: A
Correct answer: 1 and 2 only
Statements 1 and 2 define the two correctly: a residual property is the departure of a real fluid from the ideal *gas* at the same conditions, and an excess property the departure of a real solution from the ideal *solution*. Statement 3 collapses that distinction. The reference states are different, which is why residual properties are computed from an equation of state and excess properties from an activity coefficient model.
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The difference between the heat capacity at constant pressure and that at constant volume for an ideal gas is
Answer: B
Heating at constant pressure must also supply the work of expansion, and for an ideal gas that difference comes out exactly as the gas constant. For real fluids the difference depends on expansivity and compressibility.
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A gas has a constant-pressure heat capacity of 29 joules per mole kelvin and behaves ideally. What is its constant-volume heat capacity, taking the gas constant as 8.3?
Answer: C
Subtracting the gas constant from twenty-nine gives twenty point seven joules per mole kelvin. Adding rather than subtracting is the usual slip, and it can be caught by remembering that the constant volume value is always the smaller.
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Assertion (A): For a real fluid the difference between the two heat capacities is expressed using expansivity and compressibility.
Reason (R): The general relation follows from a Maxwell relation and reduces to the gas constant for an ideal gas.
Answer: D
Both are true and the reason connects the general and the special case: the ideal gas result is not a separate rule but the limit of the general one when the equation of state is simple. Expansivity and compressibility are both measurable quantities.
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