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[1] [9] According to this, the mixing temperature is the weighted arithmetic mean of the temperatures of the two initial components. Richmann's rule of mixing can also be applied in reverse, for example, to the question of the ratio in which quantities of water of given temperatures must be mixed to obtain water of a desired temperature.
The volume of such a mixture is slightly less than the sum of the volumes of the components. Thus, by the above definition, the term "40% alcohol by volume" refers to a mixture of 40 volume units of ethanol with enough water to make a final volume of 100 units, rather than a mixture of 40 units of ethanol with 60 units of water.
The number of moles of ethanol is 0.2 kg / (0.04607 kg/mol) = 4.341 mol, so that the apparent molar volume is 0.2317 L / 4.341 mol = 0.0532 L / mol = 53.2 cc/mole (1.16 cc/g). However pure ethanol has a molar volume at this temperature of 58.4 cc/mole (1.27 cc/g). If the solution were ideal, its volume would be the sum of the unmixed components ...
The ideal gas equation can be rearranged to give an expression for the molar volume of an ideal gas: = = Hence, for a given temperature and pressure, the molar volume is the same for all ideal gases and is based on the gas constant: R = 8.314 462 618 153 24 m 3 ⋅Pa⋅K −1 ⋅mol −1, or about 8.205 736 608 095 96 × 10 −5 m 3 ⋅atm⋅K ...
When one mole of water is added to a large volume of water at 25 °C, the volume increases by 18 cm 3. The molar volume of pure water would thus be reported as 18 cm 3 mol −1. However, addition of one mole of water to a large volume of pure ethanol results in an increase in volume of only 14 cm 3. The reason that the increase is different is ...
Later, in 1802, Joseph Louis Gay-Lussac published results of similar experiments, indicating a linear relationship between volume and temperature: =. Dalton's law (1801) of partial pressure states that the pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.
The partial volume of a particular gas is a fraction of the total volume occupied by the gas mixture, with unchanged pressure and temperature. In gas mixtures, e.g. air, the partial volume allows focusing on one particular gas component, e.g. oxygen.
It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. [1] In an alloy or a mixture with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the mass fraction of the α phase is