Ethylene glycol, C2H6O2, is a colorless liquid used as auto-mobile antifreeze. If the density at 20 °C of a 4.028 m solu- tion of ethylene glycol in water is 1.0241 g/mL, what is the molarity of the solution? The molar mass of ethylene glycol is 62.07 g/mol

Verified step by step guidance

1. First, let's understand what molarity is. Molarity (M) is the number of moles of solute per liter of solution. It's a measure of the concentration of a solute in a solution.
2. Next, we need to find the mass of the ethylene glycol in the solution. The molality (m) is given as 4.028 m, which means there are 4.028 moles of ethylene glycol in 1 kg of water. Since the density of the solution is given as 1.0241 g/mL, we can convert this to kg/L by multiplying by 1000, giving us 1024.1 kg/L. This is the mass of the solution (water + ethylene glycol) in 1 L.
3. Then, we need to find the mass of the water in the solution. We know that 4.028 moles of ethylene glycol is in 1 kg of water. Using the molar mass of ethylene glycol (62.07 g/mol), we can find the mass of the ethylene glycol in the solution. Multiply the number of moles by the molar mass to get the mass in grams, and then convert to kilograms by dividing by 1000.
4. Now, subtract the mass of the ethylene glycol from the total mass of the solution to find the mass of the water. Remember that the total mass of the solution is the mass of the water plus the mass of the ethylene glycol.
5. Finally, to find the molarity, divide the number of moles of ethylene glycol by the volume of the solution in liters. The volume of the solution can be found by dividing the mass of the water by the density of water (1 g/mL or 1000 kg/L).

Key Concepts

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in units of moles per liter (mol/L). To calculate molarity, you need to know the amount of solute in moles and the total volume of the solution in liters. This concept is crucial for understanding how concentrated a solution is and for performing stoichiometric calculations.

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 the solution allows us to convert the mass of the solution into volume, which is necessary for calculating molarity. Understanding density is essential for relating mass and volume in solution chemistry.

Molality

Molality is a concentration measure defined as the number of moles of solute per kilogram of solvent. It is expressed in moles per kilogram (mol/kg). In this problem, the solution's molality is given, which is important for determining the amount of solute present in a specific mass of solvent. Molality is particularly useful in colligative property calculations and when temperature changes affect volume.