The apparent molal heat capacity, enthalpy, and free energy of seawater fit to the Pitzer equations

Frank J Millero, Denis Pierrot

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The thermochemical properties (osmotic coefficient, enthalpy and heat capacity) of seawater from S=0 to 120 and 0 to 200°C have been fit to the Pitzer equations. The osmotic coefficient (φ), apparent molal heat capacity (φCp) and relative enthalpy (φL) have been fit to equations of the form φSS-1=(1/m){-AφI 1.5/(1+1.2I0.5)+m(BSSφ+mC SSφ)}φCpSS-C̄p ss0=AJ{I/(1.2m)}ln(1+1.2I0.5) +2RTm(BSSJ+mCSSJ) φLSS=(AHI/1.2m)ln(1+1.2I 0.5)-2RTm(BSSL+mCSSL)where I is the ionic strength, m is the molality of sea salt (m=∑mi, i is an ion); AX (X=φ, J and H) is the Debye-Hückel slope, and C̄pss0 is the apparent molal heat capacity of sea salt in water. The Pitzer parameters B SSX and CSSX for sea salt have been fit to functions of temperature in the form YSSX= ∑aij(T-TR)iwhere aij are adjustable parameters, YSSX is the Pitzer coefficient, T is the temperature in K, and TR=273.15 K). The standard deviations of the seawater fits were 0.0006 J g-1 K-1 for the heat capacity from 0 to 40°C and 0.0038 J g-1 K-1 from 0 to 200°C. The extrapolated values of C̄pss0 from 0 to 200°C were in reasonable agreement with the values determined from the major sea salts. The combined cp data have been fit to equations that are consistent with the theoretical values of C̄pss0. By appropriate integration of φCpSS, the apparent molal enthalpy at 298 K and osmotic coefficients at 273 K, equations were determined for all the thermochemical properties as a function of ionic strength and temperature. The thermochemical properties determined in this manner are in good agreement with direct measurements at different salinities and temperatures. The equations can be used to determine all the thermochemical properties of seawater from 0 to 200°C and I=0 to 2.4 (S=120).

Original languageEnglish (US)
Pages (from-to)81-99
Number of pages19
JournalMarine Chemistry
Volume94
Issue number1-4
DOIs
StatePublished - Mar 1 2005

Fingerprint

heat capacity
enthalpy
Seawater
Free energy
Specific heat
sea salt
Enthalpy
Salts
seawater
Ionic strength
energy
Temperature
temperature
Blind source separation
Ions
Water
salinity
ion
water
parameter

Keywords

  • Apparent molal enthalpies
  • Apparent molal heat capacity
  • Free energies
  • Osmotic coefficients
  • Pitzer equations
  • Sea salts
  • Seawater

ASJC Scopus subject areas

  • Chemistry(all)
  • Oceanography

Cite this

The apparent molal heat capacity, enthalpy, and free energy of seawater fit to the Pitzer equations. / Millero, Frank J; Pierrot, Denis.

In: Marine Chemistry, Vol. 94, No. 1-4, 01.03.2005, p. 81-99.

Research output: Contribution to journalArticle

Millero, Frank J ; Pierrot, Denis. / The apparent molal heat capacity, enthalpy, and free energy of seawater fit to the Pitzer equations. In: Marine Chemistry. 2005 ; Vol. 94, No. 1-4. pp. 81-99.
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N2 - The thermochemical properties (osmotic coefficient, enthalpy and heat capacity) of seawater from S=0 to 120 and 0 to 200°C have been fit to the Pitzer equations. The osmotic coefficient (φ), apparent molal heat capacity (φCp) and relative enthalpy (φL) have been fit to equations of the form φSS-1=(1/m){-AφI 1.5/(1+1.2I0.5)+m(BSSφ+mC SSφ)}φCpSS-C̄p ss0=AJ{I/(1.2m)}ln(1+1.2I0.5) +2RTm(BSSJ+mCSSJ) φLSS=(AHI/1.2m)ln(1+1.2I 0.5)-2RTm(BSSL+mCSSL)where I is the ionic strength, m is the molality of sea salt (m=∑mi, i is an ion); AX (X=φ, J and H) is the Debye-Hückel slope, and C̄pss0 is the apparent molal heat capacity of sea salt in water. The Pitzer parameters B SSX and CSSX for sea salt have been fit to functions of temperature in the form YSSX= ∑aij(T-TR)iwhere aij are adjustable parameters, YSSX is the Pitzer coefficient, T is the temperature in K, and TR=273.15 K). The standard deviations of the seawater fits were 0.0006 J g-1 K-1 for the heat capacity from 0 to 40°C and 0.0038 J g-1 K-1 from 0 to 200°C. The extrapolated values of C̄pss0 from 0 to 200°C were in reasonable agreement with the values determined from the major sea salts. The combined cp data have been fit to equations that are consistent with the theoretical values of C̄pss0. By appropriate integration of φCpSS, the apparent molal enthalpy at 298 K and osmotic coefficients at 273 K, equations were determined for all the thermochemical properties as a function of ionic strength and temperature. The thermochemical properties determined in this manner are in good agreement with direct measurements at different salinities and temperatures. The equations can be used to determine all the thermochemical properties of seawater from 0 to 200°C and I=0 to 2.4 (S=120).

AB - The thermochemical properties (osmotic coefficient, enthalpy and heat capacity) of seawater from S=0 to 120 and 0 to 200°C have been fit to the Pitzer equations. The osmotic coefficient (φ), apparent molal heat capacity (φCp) and relative enthalpy (φL) have been fit to equations of the form φSS-1=(1/m){-AφI 1.5/(1+1.2I0.5)+m(BSSφ+mC SSφ)}φCpSS-C̄p ss0=AJ{I/(1.2m)}ln(1+1.2I0.5) +2RTm(BSSJ+mCSSJ) φLSS=(AHI/1.2m)ln(1+1.2I 0.5)-2RTm(BSSL+mCSSL)where I is the ionic strength, m is the molality of sea salt (m=∑mi, i is an ion); AX (X=φ, J and H) is the Debye-Hückel slope, and C̄pss0 is the apparent molal heat capacity of sea salt in water. The Pitzer parameters B SSX and CSSX for sea salt have been fit to functions of temperature in the form YSSX= ∑aij(T-TR)iwhere aij are adjustable parameters, YSSX is the Pitzer coefficient, T is the temperature in K, and TR=273.15 K). The standard deviations of the seawater fits were 0.0006 J g-1 K-1 for the heat capacity from 0 to 40°C and 0.0038 J g-1 K-1 from 0 to 200°C. The extrapolated values of C̄pss0 from 0 to 200°C were in reasonable agreement with the values determined from the major sea salts. The combined cp data have been fit to equations that are consistent with the theoretical values of C̄pss0. By appropriate integration of φCpSS, the apparent molal enthalpy at 298 K and osmotic coefficients at 273 K, equations were determined for all the thermochemical properties as a function of ionic strength and temperature. The thermochemical properties determined in this manner are in good agreement with direct measurements at different salinities and temperatures. The equations can be used to determine all the thermochemical properties of seawater from 0 to 200°C and I=0 to 2.4 (S=120).

KW - Apparent molal enthalpies

KW - Apparent molal heat capacity

KW - Free energies

KW - Osmotic coefficients

KW - Pitzer equations

KW - Sea salts

KW - Seawater

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