Problem 77 - Chemistry The Central Science

Question

Glycerol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3},\) is a substance used extensively in the manufacture of cosmetic s, foodstuffs, antifreeze, and plastics. Glycerol is a water-soluble liquid with a density of 1.2656 \(\mathrm{g} / \mathrm{mL}\) at \(15^{\circ} \mathrm{C}\) . Calculate the molarity of a solution of glycerol made by dissolving 50.000 \(\mathrm{mL}\) glycerol at \(15^{\circ} \mathrm{C}\) in enough water to make 250.00 \(\mathrm{mL}\) of solution.

Step-by-Step Solution

Answer

The molarity of the glycerol solution can be calculated using the following steps: 1. Calculate the mass of glycerol: Mass = (1.2656 g/mL) × (50.000 mL) = 63.280 g 2. Calculate the molecular weight of glycerol: (3 × 12.01 g/mol) + (8 × 1.01 g/mol) + (3 × 16.00 g/mol) = 92.09 g/mol 3. Calculate the moles of glycerol: Moles = 63.280 g / 92.09 g/mol = 0.6869 mol 4. Convert the volume of the solution to liters: 250.00 mL = 250.00 / 1000 L = 0.2500 L 5. Calculate the molarity of the glycerol solution: Molarity = 0.6869 mol / 0.2500 L = 2.748 M

Step 1: Find the mass of glycerol

Given, the density of glycerol at \(15^{\circ} \mathrm{C}\) is 1.2656 \(\mathrm{g} / \mathrm{mL}\). We are given 50.000 mL of glycerol. We can calculate the mass of glycerol using the formula: Mass = Density × Volume Mass = (1.2656 \(\mathrm{g} / \mathrm{mL}\)) × (50.000 \(\mathrm{mL}\))

Step 2: Calculate moles of glycerol

To find the moles of glycerol, we need to know the molecular weight of glycerol (\(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}\)). The molecular weights of carbon (C), hydrogen (H), and oxygen (O) are 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively. Molecular weight of glycerol = (3 × 12.01 g/mol) + (8 × 1.01 g/mol) + (3 × 16.00 g/mol) Now, we can calculate the moles of glycerol using the formula: Moles = Mass / Molecular weight

Step 3: Calculate the molarity of the glycerol solution

Molarity is defined as the number of moles of solute present in 1 liter of solution. To calculate the molarity of the glycerol solution, we need to divide the moles of glycerol (calculated in step 2) by the total volume of the solution (250.00 mL) in liters. Molarity = Moles of glycerol / Total volume of the solution (in liters)

Step 4: Convert the volume of the solution to liters

Given the total volume of the solution is 250.00 mL, we need to convert it to liters. 1 L = 1000 mL So, 250.00 mL = 250.00 / 1000 L Now, plug in the moles of glycerol and the total volume of the solution in liters into the molarity formula from step 3 to get the answer.