Question

A quantity of \(10 \mathrm{~g}\) of acetic acid is dissolved in \(100 \mathrm{~g}\) of each of the following solvents. In which solvent, the mole fraction of solute is maximum? Assume no any dissociation or association of acetic acid in the solvent. (a) Water (b) Ethanol (c) Benzene (d) Same in all solvents

Short answer

Answer: The mole fraction of acetic acid is the highest in benzene.

Step-by-step solution

Calculate moles of acetic acid

To calculate the moles of acetic acid, we need to use the formula: Moles = mass / molar mass The given mass of acetic acid is 10 g. The molar mass of acetic acid (CH3COOH) can be calculated by adding the atomic masses of all the atoms in the molecule (12.01 for C, 1.01 for H, and 16 for O). So, the molar mass of acetic acid is: (2 × 12.01) + (4 × 1.01) + (2 × 16) = 60.05 g/mol Now, we can calculate the moles of acetic acid: Moles_acetic_acid = 10 g / 60.05 g/mol = 0.1664 mol

Calculate moles of each solvent

We need to calculate the moles of each solvent using the same formula as in step 1: Moles = mass / molar mass For each solvent, the given mass is 100 g. We'll calculate the moles of each solvent: (a) Water (H2O): molar mass = (2 × 1.01) + 16 = 18.02 g/mol Moles_water = 100 g / 18.02 g/mol = 5.5494 mol (b) Ethanol (C2H5OH): molar mass = (2 × 12.01) + (6 × 1.01) + 16 = 46.07 g/mol Moles_ethanol = 100 g / 46.07 g/mol = 2.1697 mol (c) Benzene (C6H6): molar mass = (6 × 12.01) + (6 × 1.01) = 78.12 g/mol Moles_benzene = 100 g / 78.12 g/mol = 1.2804 mol

Calculate mole fractions

To calculate the mole fractions, we divide the moles of acetic acid by the total moles for each solvent-acetic acid combination: Mole_fraction_water = Moles_acetic_acid / (Moles_acetic_acid + Moles_water) = 0.1664 / (0.1664 + 5.5494) = 0.02907 Mole_fraction_ethanol = 0.1664 / (0.1664 + 2.1697) = 0.07128 Mole_fraction_benzene = 0.1664 / (0.1664 + 1.2804) = 0.11494

Compare the mole fractions

Now that we have calculated the mole fractions of acetic acid in each solvent, we can compare them: Mole_fraction_water = 0.02907 Mole_fraction_ethanol = 0.07128 Mole_fraction_benzene = 0.11494 Seeing these values, we can conclude that the mole fraction of acetic acid is the highest in benzene. Therefore, the correct answer is (c) Benzene.

Key concepts

Mole Calculation

Understanding mole calculations is a fundamental aspect of chemistry that allows us to quantify substances on the molecular level. The mole is a unit of measurement for amount of substance, defined as the amount that contains the same number of entities as there are atoms in exactly 12 grams of carbon-12. This number is Avogadro's number, approximately \(6.022 \times 10^{23}\) entities.

The formula for calculating moles from mass is simply divided by the molar mass of the substance: \(\text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\). In our exercise, for acetic acid with a mass of 10g, this calculation was pivotal.

Why It's Important

Not only does mole calculation help in determining the chemical composition of a mixture, but it also sets the stage for finding out concentration, reacting ratios in stoichiometry, and producing predictions for theoretical yields. A good grip on converting mass to moles and vice versa is essential for any student venturing into chemical sciences or related fields.

Molar Mass

Molar mass acts as a bridge between the mass of a material we can measure and the amount of molecules or atoms it comprises. It is effectively the mass of one mole of a substance, usually expressed in grams per mole (g/mol). To find the molar mass of a compound, such as acetic acid \((CH_3COOH)\), each atom's atomic mass is multiplied by its count in the molecule and summed together.

In our example, the molar mass is calculated by aggregating the atomic masses of carbon, hydrogen, and oxygen, reflecting the repetitive unit of atomic makeup within the molecule.

Practical Uses of Molar Mass

It has extensive practical uses, from converting moles to grams in laboratories to discerning the relative molecule size when comparing compounds. Students should remember that the molar mass is characteristic to each substance, just like a fingerprint, hence knowing how to calculate it is fundamental in chemistry.

Solution Concentration

When we dissolve a substance in a solvent, we develop a mixture known as a solution. The mole fraction is a way of expressing the concentration of a component in a solution. It is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution.

In mathematical terms, mole fraction \(X_i\) of a component \(i\) is given by: \(X_i = \frac{n_i}{\sum{n_i}}\), where \(n_i\) is the number of moles of the component and \(\sum{n_i}\) is the sum of moles of all the components of the solution. This calculation was key to solving our original problem, as we compared mole fractions to determine the solvent in which acetic acid's mole fraction was maximum.

Significance in Various Fields

Mole fractions are used in many fields, such as material science, pharmacology, and environmental studies, to understand the composition and behaviour of solutions. It's a dimensionless quantity which makes it useful for comparisons and theoretical applications, especially when the precise masses of solute and solvent are not known.