As an undergraduate chemical engineering student, you are involved in a summer   research project that requires you to measure the molar volume of a methanol (1) + water (2) binary system at 298.15 K along an isobar. You measure the following data, which is reported in Table 9-5 as

 

A month later, after you have finished the project and have left the facility, you get a message from your research advisor asking you to estimate (as accurately as you can) the molar volume of the methanol + water mixture with 75% by mole methanol at the same T and P of your experiment. What molar volume will you report? What are the partial molar volumes of each component at this state?

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TABLE 9-5 Molar volume for the methanol (1) + water (2) system at 298.15 K and 1 bar. 0.0545 0.1016 0.1532 0.2042 0.2516 0.2960 0.3438 0.3937 0.4396 0.5057 0.5416 0.5904 0.6450 0.6946 0.7391 0.7855 0.8388 0.8797 0.9284 1 Molar Volume (cm³/mol) 18.070 19.130 20.045 21.054 22.065 23.022 23.936 24.939 26.010 27.016 28.502 29.326 30.464 31.760 32.958 34.048 35.199 36.540 37.583 38.843 40.732 A Arce, A Blanco, A Soto and 1 Vidal: Dansities, Retractive Indices, and Excess Molar Volumes of the Based on data from Samary Systems Water Methanol +1-Octanol and Water Ethanol 1-Detand and Their Binary Mixtures at 298,15 K J.Chem.Eng Data 38 (1993) 336-340