Question

Pure acetic acid, known as glacial acetic acid, is a liquid with a density of \(1.049 \mathrm{~g} / \mathrm{mL}\) at \(25^{\circ} \mathrm{C}\). Calculate the molarity of a solution of acetic acid made by dissolving \(20.00 \mathrm{~mL}\) of glacial acetic acid at \(25^{\circ} \mathrm{C}\) in enough water to make \(250.0 \mathrm{~mL}\) of solution.

Short answer

The molarity of the acetic acid solution is 1.396 M.

Step-by-step solution

Calculate the mass of acetic acid using its density and volume

To calculate the mass of acetic acid in the given volume, we use the formula: mass = density × volume The volume of glacial acetic acid is 20.00 mL, and its density is 1.049 g/mL. Plugging in the values, we get: mass = 1.049 g/mL × 20.00 mL mass = 20.98 g So, the mass of acetic acid dissolved is 20.98 g.

Convert the mass of acetic acid to moles using its molar mass

To find the moles of acetic acid, we will use the molar mass of acetic acid: molar mass of acetic acid = 60.05 g/mol Now, we can find the moles by dividing the mass of acetic acid by its molar mass: moles of acetic acid = mass / molar mass moles of acetic acid = 20.98 g / 60.05 g/mol moles of acetic acid = 0.349 mol We have 0.349 moles of acetic acid.

Calculate the molarity using the moles of acetic acid and the final volume of the solution

Finally, we can calculate the molarity of the solution using the moles of acetic acid and the final volume of the solution: Molarity (M) = moles of solute / volume of solution (in liters) The final volume of the solution is 250.0 mL, which we need to convert to liters: 250.0 mL = 250.0 / 1000 L = 0.250 L Now, we can calculate the molarity of the solution: Molarity = 0.349 mol / 0.250 L Molarity = 1.396 mol/L Therefore, the molarity of the acetic acid solution is 1.396 M.