In modern laboratories, sophisticated instruments are used to determine molar mass. However, if you don’t have access to such an instrument, you could still determine molar mass using nothing more complicated than a thermometer and a balance. The addition of 0.24 g of sulfur to 100. g of the solvent carbon tetrachloride lowers the solvent’s freezing point by 0.28°C. Sulfur is known to exist in molecular form. What is the molar mass and molecular formula of sulfur molecules?

ANTICIPATE You might already be aware that sulfur commonly forms crownlike S₈ molecules.

PLAN Use the procedure for cryoscopy in Toolbox 5F.1. Sulfur is a nonelectrolyte, so i = 1. Once you know the molar mass of the molecules, divide it by the molar mass of sulfur atoms (found in the list of elements inside the back cover) to find how many atoms are in each molecule.

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Toolbox 5F.1 HOW TO USE COLLIGATIVE PROPERTIES TO DETERMINE MOLAR MASS CONCEPTUAL BASIS The lowering of freezing point and the generation of osmotic pressure both depend on the total concentration of solute parti- cles. Therefore, by using these colligative properties to deter- mine the amount of solute present and knowing its mass, its molar mass can be inferred. PROCEDURE 1. Cryoscopy Step 1 Convert the observed freezing-point depression, AT₁ into solute molality b (Topic 5E) by writing Eq. 1b in the form b AT₁ ik Take the freezing-point constant from Table 5F.1. Step 2 Calculate the amount of solute, nolute (in moles), in the sample by multiplying the molality by the mass of solvent, msolvent (in kilograms): nsolute = b x m solvent Step 3 Determine the molar mass of the solute by dividing the given mass of solute, Msolute (in grams), by the calculated amount in moles (step 2). m solute Msolute nsolute This procedure is illustrated in Example 5F.1. 2. Osmometry Step 1 Convert the observed osmotic pressure into solute molar concentration (c) by writing Eq. 3 in the form II iRT In some cases, it may be necessary to calculate the osmotic pressure from the height, h, of the solution (in an apparatus like that in Fig. 5F.3) by using II = gdh, where d is the density of the solution and g is the acceleration of free fall (see inside back cover). Step 2 Because molar concentration is defined as c = 1solute/V, where nsolute is the amount of solute (in moles) and V is the volume of solution (in liters), calculate the amount of solute from nsolute = CV Step 3 Determine the molar mass of the solute by dividing the given mass of solute, msolute (in grams), by its amount (step 2), as in the procedure for cryoscopy. This procedure is illustrated in Example 5F.2.