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Enthalpy of Mixing

The enthalpy of mixing (also called heat of mixing) is the heat that is absorbed or released upon mixing of two (non-reacting) chemical substances. Enthalpy of mixing can often be ignored in calculations for mixtures where other heat terms exist, or in cases where the mixture is ideal. The sign convention is the same as for enthalpy of reaction: when the enthalpy of mixing is positive, mixing is endothermic while negative enthalpy of mixing signifies exothermic mixing. In ideal mixtures the enthalpy of mixing is null. In non-ideal mixtures the thermodynamic activity of each component is different from its concentration by multiplying with the activity coefficient.

Formal Definition

For a liquid, enthalpy of mixing can be defined as follows

$H_{mixture}=\Delta H_{mix}+\sum X_{i}H_{i}$

Where:

• H_mixture is the total enthalpy of the system after mixing
• ΔH_mix is the enthalpy of mixing
• x_i is the mole fraction of component i in the system

• H_i is the enthalpy of pure i

Enthalpy of mixing can also be defined using Gibbs free energy of mixing

G_mix=H_mix-T*S_mix

It should be noted that enthalpy of mixing is defined exclusively for the continuum regime, which excludes molecular-scale effects (However, first-principles calculations have been made for some metal-alloy systems such as Al-Co-Cr or β-Ti).

Measurement Apparatus

Lukas, Hans Leo Fries, Suzana G. Sundman, Bo. (2007). Computational Thermodynamics - The Calphad Method - 4.1.1.1 Mixing and Reaction Calorimetry. Cambridge University Press. Online version available at:

http://app-knovel-com.offcampus.lib.washington.edu/hotlink/pdf/id:kt007V0J22/computational-thermodynamics/mixing-reaction-calorimetry (page 60 onward)

Berthelot was one of the first to use what could be called a "modern" calorimeter, used to study enthalpy of formation of compounds. more stuff at this link "A Dictionary of Chemistry and the Allied Branches of Other Sciences, Part 2" https://books.google.com/books?id=NfMfAQAAMAAJ&pg=PA997&lpg=PA997&dq=Berthelot+heat+of+mixing&source=bl&ots=aXERgJIA9n&sig=40pZDU5rKs2ZdyV0Py0kdQNIkNA&hl=en&sa=X&ved=0ahUKEwic1vTA953SAhVW3mMKHfwpD0kQ6AEIITAB#v=onepage&q=Berthelot%20heat%20of%20mixing&f=false

Ideal Mixtures

An ideal mixture is any in which the arithmetic mean (with respect to mole fraction) of the two pure substances is the same as that of the final mixture. Among other important thermodynamic simplifications, this means that enthalpy of mixing is zero. Any gas that follows the ideal gas law can be assumed to mix ideally, as can hydrocarbons and liquids with similar molecular interactions and properties.

References

For the formal definition section: Sinnott, Ray K. Towler, Gavin. (2009). Chemical Engineering Design - SI Edition (5th Edition) - 3.8 Enthalpy of Mixtures. Elsevier. Online version available at:

http://app-knovel-com.offcampus.lib.washington.edu/hotlink/pdf/id:kt00ANSQ3L/chemical-engineering/enthalpy-of-mixtures

Links to follow up on

A flow calorimeter for enthalpies of mixing (comment on "static" calorimeters): https://doc.rero.ch/record/8247/files/St_ckli_Fritz_-_A_flow_calorimeter_for_enthalpies_of_mixing_20071030.pdf

Early flow calorimeter use http://pubs.acs.org/doi/pdf/10.1021/je60029a003