At 25 °C, the density of a 50 % (by mass) ethanol/water solution is 0.914 g/cc. Given that the partial molar volume of water in the solution is 17.4 cc/mol, what is the partial molar volume of the ethanol?
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Well, I could tell you the answer, but I must warn you, it's quite "spirited"! 😄 The partial molar volume of ethanol in the solution is approximately 16.0 cc/mol. Looks like ethanol is dancing its way through that solution! 🍹💃
To find the partial molar volume of ethanol in the solution, we can use the formula:
Partial molar volume of a component = ((Density of the solution - Density of the pure solvent) / Molar concentration of the component) - Partial molar volume of the other component
Let's calculate the partial molar volume of ethanol step-by-step:
Step 1: Calculate the molar concentration of ethanol in the solution:
Mass fraction of ethanol = 50% = 0.5
Mass of ethanol in the solution = (Density of the solution) * (Volume of the solution)
Volume of the solution = 1 cc (since the density is given in g/cc)
Mass of ethanol in the solution = 0.914 g/cc * 1 cc = 0.914 g
Molar mass of ethanol = 46.07 g/mol (approx)
Moles of ethanol in the solution = (Mass of ethanol in the solution) / (Molar mass of ethanol)
Moles of ethanol in the solution = 0.914 g / 46.07 g/mol ≈ 0.01986 mol
Molar concentration of ethanol = (Moles of ethanol in the solution) / (Volume of the solution)
Molar concentration of ethanol = 0.01986 mol / 1 cc ≈ 0.01986 M (molar)
Step 2: Calculate the partial molar volume of ethanol:
Partial molar volume of ethanol = ((Density of the solution - Density of the pure solvent) / Molar concentration of ethanol) - Partial molar volume of water
The density of pure water at 25 °C is approximately 0.997 g/cc.
Partial molar volume of ethanol = ((0.914 g/cc - 0.997 g/cc) / 0.01986 M) - 17.4 cc/mol
Partial molar volume of ethanol = (-0.083 g/cc / 0.01986 M) - 17.4 cc/mol
Partial molar volume of ethanol ≈ -4.179 cc/mol (approximately)
Therefore, the partial molar volume of ethanol in the solution is approximately -4.179 cc/mol.
To find the partial molar volume of ethanol in the solution, we can make use of the formula:
Partial molar volume of a component (in this case, ethanol) = Density / (Concentration * Molar mass)
Here, we are given the density of the solution as 0.914 g/cc, and we know that it is a 50% (by mass) ethanol/water solution. This means that the concentration of ethanol in the solution is 50% by mass.
The molar mass of ethanol (CH3CH2OH) is approximately 46.07 g/mol.
So, let's calculate the partial molar volume of ethanol step-by-step:
Step 1: Calculate the concentration of ethanol in the solution in g/cc.
Concentration of ethanol = 50% * Density of solution
Concentration of ethanol = 0.5 * 0.914 g/cc
Step 2: Convert the concentration of ethanol to mol/cc.
Concentration of ethanol (mol/cc) = Concentration of ethanol (g/cc) / Molar mass of ethanol
Concentration of ethanol (mol/cc) = (0.5 * 0.914 g/cc) / 46.07 g/mol
Step 3: Calculate the partial molar volume of ethanol.
Partial molar volume of ethanol = Density of solution / (Concentration of ethanol * Molar mass of ethanol)
Partial molar volume of ethanol = 0.914 g/cc / ((0.5 * 0.914 g/cc) / 46.07 g/mol)
By simplifying this equation, we can find the partial molar volume of ethanol.