Glycerol, C3H8O3, is a substance used extensively in the manufacture of cosmetics, foodstuffs, antifreeze, and plastics. Glycerol is a water-soluble liquid with a density of 1.2656 g/mL at 15 °C. Calculate the molarity of a solution of glycerol made by dissolving 50.000 mL glycerol at 15 °C in enough water to make 250.00 mL of solution.

Verified step by step guidance

Calculate the mass of glycerol using its volume and density: \( \text{mass} = \text{density} \times \text{volume} \).

Convert the mass of glycerol to moles using its molar mass: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). The molar mass of glycerol (C3H8O3) is calculated by adding the atomic masses of its constituent atoms.

Determine the volume of the solution in liters by converting 250.00 mL to liters: \( \text{volume in liters} = \frac{250.00 \text{ mL}}{1000} \).

Calculate the molarity of the glycerol solution using the formula: \( \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \).

Combine the results from the previous steps to express the molarity of the glycerol solution.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L). To calculate molarity, one must know the amount of solute in moles and the total volume of the solution in liters. This concept is essential for understanding how concentrated a solution is and is commonly used in chemistry for preparing solutions.

Density

Density is the mass of a substance per unit volume, typically expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³). In this context, the density of glycerol allows us to convert its volume into mass, which is necessary for calculating the number of moles of glycerol present in the solution. Understanding density is crucial for accurately determining the amount of solute in a given volume.

Molecular Weight

Molecular weight, or molar mass, is the mass of one mole of a substance, measured in grams per mole (g/mol). For glycerol (C3H8O3), the molecular weight can be calculated by summing the atomic weights of its constituent atoms: carbon, hydrogen, and oxygen. This value is vital for converting grams of glycerol into moles, which is a necessary step in calculating the molarity of the solution.

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