1.23.2: Water: Molar Volume
- Page ID
- 397799
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The molar volume \(\mathrm{V}_{1}^{*}(\ell)\) and density \(\rho_{1}^{*}(\ell)\) of water(\(\ell\)) are intensive properties. The \(\mathrm{p}-\mathrm{V}-\mathrm{T}\) properties of water are perhaps the most extensively studied. Two properties are almost universally known;
- the molar volume of water at ambient pressure and \(273.15 \mathrm{~K}\) is less than that of ice, and
- the molar volume of water at \(273.15 \mathrm{~K}\) decreases on heating to reach a TMD before increasing.
At ambient pressure the temperature of maximum density for water, \(\mathrm{TMD} = 3.98 \text { Celsius}\); for \(\mathrm{D}_{2}\mathrm{O}\), \(\mathrm{TMD} = 11.44 \text { Celsius}\). The \(\mathrm{TMD}\) for \(\mathrm{SiO}_{2}\) is around 15270 Celsius, the dependence of density on temperature being less marked about the \(\mathrm{TMD}\) than that for water [1].
The dependence of \(\mathrm{V}^{*}\left(\mathrm{H}_{2} \mathrm{O} ; \ell\right)\) on temperature and pressure is reported by many laboratories. Most accounts cite the study reported by Kell and Whalley in 1965, later extended in 1978 [2,3]. Kell has examined the results in detail [4]. The \(\mathrm{TMD}\) has, of course, attracted considerable attention. Nevertheless the \(\mathrm{TMD}\) has no deep significance in the context of understanding the properties of water(\(\ell\)). Other properties of water(\(\ell\)) show extrema at other temperatures; e.g. isothermal compressibility near \(300 \mathrm{~K}\) [5-7].
Footnotes
[1] C. A. Angell and H. Kanno, Science, 1976,193,1121.
[2] G. S. Kell and E. Whalley, Philos. Trans. R. Soc. London, 1965,258,565.
[3] G. S. Kell, G. M. McLaurin and E.Whalley, Proc. R. Soc. London, Ser. A,1978,360,389.
[4] G. S. Kell, J. Chem. Eng. Data, 1967,12,66; 1975,20,97; 1970,15,119.
[5] R.A. Fine and F. J. Millero, J.Chem.Phys.,1975,63,89; 1973,59,5529.
[6] D.-P. Wang and F. J. Millero, J.Geophys. Res., 1973,78,7122.
[7] F. J. Millero, R. W. Curry and W. Drost-Hansen, J. Chem. Eng. Data, 1969, 14,422.