User:Ychzhang17/sandbox

The heat of dilution, or enthalpy of dilution, refers to the enthalpy change associated with the dilution process of a component in a solution at a constant pressure. If the initial state of the component is a pure liquid (presuming the solution is liquid), the dilution process is equal to its dissolution process and the heat of dilution is the same as the heat of solution. Generally, the heat of dilution is normalized by the mole number of the solution and its dimension is energy per unit mass, commonly expressed in the unit of kJ/mol (or J/mol).

Definition

The heat of dilution can be defined from two perspectives: the differential heat and the integral heat. The differential heat of dilution is viewed on a micro scale, which is associated with the process in which a small amount of concentrated solution is added to the mass dilute solution. The molar differential heat of dilution is thus defined as the enthalpy change caused by adding a mole of a concentrated solution at a constant temperature and pressure. Because of the small amount of addition, the concentration of dilute solution remains unchanged. Mathematically, the molar differential heat of dilution is denoted as^[1]:

${\begin{aligned}\ \ \ \ \ \ \ \ \Delta _{dil}H=\left({\frac {\partial H}{\partial \xi }}\right)_{T,p,n_{B}}\end{aligned}}$

where ξ is the mole number of the dilution.

The integral heat of dilution, however, is viewed on a macro scale. With respect to the integral heat, we consider a process in which a certain amount of solution diluted from an initial concentration to a final concentration. The enthalpy change in this process, normalized by the mole number, is evaluated as the molar integral heat of dilution. Mathematically, the molar integral heat of dilution is denoted as:

${\begin{aligned}\ \ \ \ \ \ \ \ \Delta _{m}H(dil)={\frac {\Delta H(dil)}{n_{B}}}\end{aligned}}$

Dilution and Dissolution

The process of dissolution and the process of dilution are closely related to each other. In both processes, similar final statuses of solutions are reached. However, the initial statuses can be different. In a dissolution process, a solute is changed from a pure phase—solid, liquid, or gas—to a solution phase. If the pure phase of the solute is a solid or gas (presuming the solvent itself is liquid), the process can be seen in two stages: the phase change into a liquid, and the mixing of liquids. The dissolution process is generally expressed as:

${\begin{aligned}\ \ \ \ \ \ \ \ {\textrm {solute(s,l,g)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}\end{aligned}}$

The notation "sln" stands for "solution", which represents a status of the solvent or solute being part of the solution.

In a dilution process, on the other hand, the solution is changed from one concentration to another, illustrated as:

${\begin{aligned}\ \ \ \ \ \ \ \ \ \ {\textrm {solute(sln}}_{1}{\textrm {)}}+{\textrm {solvent(sln}}_{1}{\textrm {)}}\rightarrow {\textrm {solute(sln}}_{2}{\textrm {)}}+{\textrm {solvent(sln}}_{2}{\textrm {)}}\end{aligned}}$

Consider an extreme condition for the dilution process. Let the initial status be the pure liquid. The dilution process is then described as:

${\begin{aligned}\ \ \ \ \ \ \ \ \ {\textrm {solute(l)}}+{\textrm {solvent(l)}}\rightarrow {\textrm {solute(sln)}}+{\textrm {solvent(sln)}}\end{aligned}}$

It is worth noting that this expression is just the second stage of the dissolution process. In other words, if both the solute to be dissolved and the initial "solution" to be diluted are liquids, the dissolution and the dilution processes are identical.

Causes

Viewed from a microscopic perspective, the dilution process involves three steps of molecular interaction: the breaking of attraction between solute molecules, the breaking of attraction between solvent molecules, and the forming of attraction between a solute and a solvent molecule. If the solution is ideal, which means the solute and the solvent are identical in an interaction, then all the kinds of attraction mentioned above have the same value. As a result, the enthalpy change caused by breaking and forming attraction is canceled, and the dilution of an ideal solution causes no enthalpy change^[2].

However, if the solute and solvent cannot be treated identically when considered in terms of molecular attraction, which makes the solution non-ideal, the net change of enthalpy is nonzero. In other words, the heat of dilution results from the non-ideality of the solution.

Examples for acids

The heats of solution of some acids in aqueous solutions are shown in the following table^[3].

$-\Delta _{dil}H$ in kJ/mol at 25°C
m	Dil. ratio	HF	HCl	HClO₄	HBr	HI	HNO₃	CH₂O₂	C₂H₄O₄
55.506	1.0		45.61		48.83		19.73	0.046	2.167
5.5506	10	13.66	5.841	-0.490	4.590	3.577	1.540	0.285	1.477
0.5551	100	13.22	1.234	0.050	0.983	0.736	0.502	0.184	0.423
0.0555	1000	12.42	0.427	0.259	0.385	0.351	0.318	0.121	0.272
0.00555	10000	8.912	0.142	0.126	0.130	0.121	0.130	0.105	0.243
0.000555	100000	3.766	0.042	0.042	0.038	0.038	0.046	0.054	0.209
0	∞	0	0	0	0	0	0	0	0

References

^ H. DeVoe, "Reactions of other chemical processes," in Thermodynamics and Chemistry, 2nd ed. London, UK: Pearson Education, 2001, pp. 303-366.
^ P. Atkins and J. D. Paula, "Simple mixtures," in Physical Chemistry, 8th ed. New York: W.H. Freeman and Company, 2006, pp. 137-173.
^ V. B. Park, "Heats of dilution," in Thermal Properties of Aqueous Uni-Univalent Electrolytes, Washington DC: U.S. Government Printing Office, 1965, pp. 10-19.

Ychzhang17 (talk) 01:51, 28 April 2017 (UTC)

[1] H. DeVoe, "Reactions of other chemical processes," in Thermodynamics and Chemistry, 2nd ed. London, UK: Pearson Education, 2001, pp. 303-366.

[2] P. Atkins and J. D. Paula, "Simple mixtures," in Physical Chemistry, 8th ed. New York: W.H. Freeman and Company, 2006, pp. 137-173.

[3] V. B. Park, "Heats of dilution," in Thermal Properties of Aqueous Uni-Univalent Electrolytes, Washington DC: U.S. Government Printing Office, 1965, pp. 10-19.

[1]

[2]

[3]