Subtopic Deep Dive

Excess Molar Volumes in Binary Liquid Mixtures
Research Guide

What is Excess Molar Volumes in Binary Liquid Mixtures?

Excess molar volumes (V^E) quantify the deviation from ideal volume additivity in binary liquid mixtures, measured via densitometry over composition and temperature ranges.

Researchers compute V^E from mixture densities using V^E = V_m - (x_1 V_1 + x_2 V_2), where V_m is molar volume of mixture and V_1, V_2 are pure component volumes. Data fitting employs Redlich-Kister polynomials: V^E = x_1 x_2 Σ A_k (x_1 - x_2)^k. Over 10 papers from 1987-2013 report V^E for systems like formamide + 2-methoxyethanol (Roy et al., 2007, 83 citations) and DMSO + o-xylene (Ciocîrlan and Iulian, 2009, 60 citations).

Curated Papers

Key Challenges

Why It Matters

Excess molar volume data inform molecular interactions for process simulation in chemical engineering, enabling accurate phase equilibrium models (Nakata and Sakurai, 1987). V^E guides solvent selection in extraction and distillation, reducing energy costs in industrial separations (Roy et al., 2007). Prigogine-Flory-Patterson theory links V^E to packing effects, aiding mixture design for pharmaceuticals and fuels (Reis et al., 2010).

Key Research Challenges

Temperature Dependence Modeling

Capturing V^E variation across wide T ranges requires extended Redlich-Kister forms, but polynomial divergence at extremes limits accuracy (Zarei and Jalili, 2006). Few studies exceed 298-343 K, hindering extrapolation (Roy et al., 2007).

Molecular Interaction Interpretation

Linking V^E to specific interactions like H-bonding or dispersion remains qualitative despite theories like Prigogine-Flory-Patterson (Reis et al., 2010). Compositional asymmetries challenge simple fitting (Ciocîrlan and Iulian, 2009).

Densitometry Precision Limits

Vibrating tube densitometers yield ρ ±0.1 kg/m³, but propagate errors in low-V^E systems near ideality (Mahajan and Mirgane, 2013). Calibration inconsistencies across labs affect reproducibility (Nakata and Sakurai, 1987).

Essential Papers

Refractive Index of Liquid Mixtures: Theory and Experiment

João Carlos R. Reis, Isabel M. S. Lampreia, Ângela F.S. Santos et al. · 2010 · ChemPhysChem · 217 citations

Abstract An innovative approach is presented to interpret the refractive index of binary liquid mixtures. The concept of refractive index “before mixing” is introduced and shown to be given by the ...

Refractive index and excess volume for binary liquid mixtures. Part 1.—Analyses of new and old data for binary mixtures

Mitsuo Nakata, Masao Sakurai · 1987 · Journal of the Chemical Society Faraday Transactions 1 Physical Chemistry in Condensed Phases · 92 citations

The relation between the refractive index and the excess molar volume for binary liquid mixtures has been clarified using the additivity rule. The excess volume is represented by two terms due to t...

Viscosity, Density, and Speed of Sound for the Binary Mixtures of Formamide with 2-Methoxyethanol, Acetophenone, Acetonitrile, 1,2-Dimethoxyethane, and Dimethylsulfoxide at Different Temperatures

Mahendra Nath Roy, Bipul Sarkar, Riju Chanda · 2007 · Journal of Chemical & Engineering Data · 83 citations

Densities and viscosities of binary liquid mixtures of formamide with 2-methoxyethanol, acetophenone, acetonitrile, 1,2-dimethoxyethane, and dimethylsulfoxide have been measured at (298.15, 308.15,...

Densities and derived thermodynamic properties of (2-methoxyethanol + 1-propanol, or 2-propanol, or 1,2-propandiol) at temperatures from T= (293.15 to 343.15) K

Hosseinali Zarei, Fatemeh Jalili · 2006 · The Journal of Chemical Thermodynamics · 78 citations

Study of Densities, Viscosities and Ultrasonic Speeds of Binary Mixtures Containing 1,2-Dimethoxyethane and an Alkan-l-ol at 298.15 K

Bhoj Bahadur Gurung, Mahendra Nath Roy · 2006 · Journal of Solution Chemistry · 71 citations

Volumetric and viscometric behaviour of binary systems: (1-hexanol + hydrocarbons)

Mohammad A. Chowdhury, Majid Mohadesi, Mohammed F. Saleh · 2001 · The Journal of Chemical Thermodynamics · 71 citations

Densities, Viscosities, Speeds of Sound, and Refractive Indices of Binary Mixtures of 1-Decanol with Isomeric Chlorotoluenes

Subhash C. Bhatia, Ruman Rani, Jasbir Sangwan et al. · 2011 · International Journal of Thermophysics · 69 citations

Reading Guide

Foundational Papers

Start with Reis et al. (2010, 217 citations) for refractive index-V^E theory linking optics to volumes; Nakata and Sakurai (1987, 92 citations) for additivity analysis of historical data; Roy et al. (2007, 83 citations) for densitometry protocols in amide systems.

Recent Advances

Mahajan and Mirgane (2013, 60 citations) for alkane+alcohol V^E at 298 K; Bhatia et al. (2011, 69 citations) for decanol+chlorotoluene properties including densities.

Core Methods

Densitometry for ρ(T,x); Redlich-Kister polynomial fitting; volume-fraction mixing rules; Prigogine-Flory-Patterson for free volume interpretation (Reis et al., 2010).

How PapersFlow Helps You Research Excess Molar Volumes in Binary Liquid Mixtures

Discover & Search

Research Agent uses searchPapers('excess molar volumes binary mixtures Redlich-Kister') to retrieve 50+ papers including Reis et al. (2010, 217 citations), then citationGraph reveals clusters around Roy et al. (2007). findSimilarPapers on Zarei and Jalili (2006) uncovers temperature-dependent studies; exaSearch queries 'V^E formamide DMSO' for niche systems.

Analyze & Verify

Analysis Agent applies readPaperContent to extract V^E data tables from Roy et al. (2007), then runPythonAnalysis fits Redlich-Kister polynomials via NumPy least-squares, verifying coefficients against reported values. verifyResponse (CoVe) cross-checks fitted V^E vs. experimental with GRADE scoring for statistical significance (p<0.05); runPythonAnalysis computes isobaric expansivities α^E from density derivatives.

Synthesize & Write

Synthesis Agent detects gaps like missing V^E for alcohol + ionic liquid systems via contradiction flagging across papers. Writing Agent uses latexEditText to format Redlich-Kister equations, latexSyncCitations integrates 20+ refs from Reis et al. (2010), and latexCompile generates publication-ready tables; exportMermaid diagrams V^E isotherms vs. composition.

Use Cases

"Fit Redlich-Kister to V^E data from Roy et al. 2007 formamide mixtures and plot residuals"

Research Agent → searchPapers → readPaperContent → Analysis Agent → runPythonAnalysis (NumPy polyfit, matplotlib residuals plot) → researcher gets fitted coefficients, RMSE=0.02 cm³/mol, residual plot.

"Write LaTeX section on V^E temperature trends with citations from Zarei 2006"

Synthesis Agent → gap detection → Writing Agent → latexEditText (insert equations) → latexSyncCitations (Zarei and Jalili 2006) → latexCompile → researcher gets compiled PDF with V^E/T contour plot.

"Find Python code for excess property calculations in binary mixture papers"

Research Agent → paperExtractUrls (Mahajan 2013) → paperFindGithubRepo → githubRepoInspect → researcher gets validated NumPy script for V^E from densities, tested on octane+octan-2-ol data.

Automated Workflows

Deep Research workflow scans 50+ papers via searchPapers → citationGraph, generating structured report ranking V^E studies by system (e.g., alcohols > amides) with GRADE scores. DeepScan's 7-step chain: readPaperContent (Ciocîrlan 2009) → runPythonAnalysis (V^E fit) → verifyResponse → exportCsv data tables. Theorizer hypothesizes V^E correlations from Prigogine-Flory-Patterson across Reis (2010) and Nakata (1987).

Try Doxa for Excess Molar Volumes in Binary Liquid Mixtures Research

Frequently Asked Questions

What defines excess molar volume in binary mixtures?

V^E = (x_1 M_1 + x_2 M_2)/ρ_m - (x_1 V_1 + x_2 V_2), computed from measured mixture density ρ_m and pure volumes V_1, V_2 (Roy et al., 2007).

What methods measure V^E?

Densitometry with vibrating tube densimeters at precise T (298-343 K), fitted by Redlich-Kister expansions up to 6th order (Zarei and Jalili, 2006).

What are key papers on V^E?

Reis et al. (2010, 217 citations) links refractive index to V^E theory; Roy et al. (2007, 83 citations) reports formamide systems; Nakata and Sakurai (1987, 92 citations) analyzes additivity rules.

What open problems exist in V^E research?

Predicting V^E from molecular simulations without empiricism; extending data to high T/P for industrial processes; resolving fitting ambiguities in near-ideal mixtures (Mahajan and Mirgane, 2013).