The temperature has a greater influence on the activity coefficient compared to pressure. The pressure dependence is not explicitly considered in the given expression, and its influence on the activity coefficient is generally smaller than that of temperature, especially at moderate pressures.
The temperature dependence of the activity coefficient (γi ) in a solution can be expressed as:
( ∂lnγi/ ∂T )P = ΔHi/ RT2
where:
ΔHi is the partial molar enthalpy of component i in the solution,
R is the gas constant,
T is the absolute temperature.
This expression is derived from the Gibbs-Duhem equation and the definition of the activity coefficient (γi ).
In the context of Example 12.2, where the pressure (P) is constant (P_0 ), the temperature dependence is given by the term
Comparing the influence of temperature and pressure on the activity coefficient, we can see that the effect of temperature is determined by the partial molar enthalpy (ΔHi ) and the absolute temperature (T) in the expression. The greater the magnitude of ΔHi , the larger the impact of temperature on the activity coefficient.
Therefore, in this context, the temperature has a greater influence on the activity coefficient compared to pressure. The pressure dependence is not explicitly considered in the given expression, and its influence on the activity coefficient is generally smaller than that of temperature, especially at moderate pressures.
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