If 291 g of a compound is added to 1.02 kg of water to increase the boiling point by 5.77^∘ C,

step 1 Here 291 gram of a compound is added to 1 .02 kilogram water and boiling point increases by 5 .7

If 291 g of a compound is added to 1.02 kg of water to...

If $291 \mathrm{~g}$ of a compound is added to $1.02 \mathrm{~kg}$ of water to increase the boiling point by $5.77^{\circ} \mathrm{C}$, what is the molar mass of the added compound? (Assume a van't Hoff factor of $1 .$ ) a. $31.1 \mathrm{~g} / \mathrm{mol}$ b. $30.3 \mathrm{~g} / \mathrm{mol}$ c. $28.5 \mathrm{~g} / \mathrm{mol}$ d. $18.3 \mathrm{~g} / \mathrm{mol}$ e. $25.3 \mathrm{~g} / \mathrm{mol}$

If $291 \mathrm{~g}$ of a compound is added to $1.02 \mathrm{~kg}$ of water to increase the boiling point by $5.77^{\circ} \mathrm{C}$, what is the molar mass of the added compound? (Assume a van't Hoff factor of $1 .$ )
a. $31.1 \mathrm{~g} / \mathrm{mol}$
b. $30.3 \mathrm{~g} / \mathrm{mol}$
c. $28.5 \mathrm{~g} / \mathrm{mol}$
d. $18.3 \mathrm{~g} / \mathrm{mol}$
e. $25.3 \mathrm{~g} / \mathrm{mol}$

Key Concepts

Colligative Properties

Colligative properties are physical properties of solutions that depend on the concentration of solute particles in a solvent rather than the identity of those particles. They include boiling point elevation, freezing point depression, vapor pressure lowering, and osmotic pressure, and are useful for determining molar masses and other properties of solutes.

Boiling Point Elevation

Boiling point elevation is a colligative property where the boiling point of a solvent increases upon the addition of a non-volatile solute. This phenomenon occurs because the presence of solute particles reduces the solvent’s vapor pressure, requiring a higher temperature to reach the vapor pressure equal to atmospheric pressure.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is particularly useful in studying boiling point elevation and freezing point depression because it remains unaffected by temperature changes, unlike molarity which is volume-based.

van't Hoff Factor

The van't Hoff factor represents the number of particles a solute generates upon dissolving in a solvent. It is crucial for adjusting colligative property calculations, as the extent of boiling point elevation or freezing point depression depends on the total number of solute particles present rather than simply the number of moles of substance added.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole. It is a fundamental property used to convert between the mass of a compound and the number of moles, thereby helping in quantifying the amount of substance involved in physical and chemical calculations such as those related to colligative properties.

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