Concentrated hydrochloric acid solution contains 37.0% by mass HCl. If the density is 1.18 g/mL, what is the molar concentration? (LO 13.6, 13.7) (a) 10.1 M (b) 16.2 M (c) 8.60 M (d) 12.0 M

Verified step by step guidance

1. Step 1: Determine the mass of HCl in 1 liter of solution. Since the solution is 37.0% HCl by mass, this means that in 100 g of solution, there are 37.0 g of HCl.
2. Step 2: Calculate the mass of 1 liter of the solution using its density. The density is given as 1.18 g/mL, so 1 liter (1000 mL) of solution has a mass of 1.18 g/mL * 1000 mL = 1180 g.
3. Step 3: Calculate the mass of HCl in 1 liter of solution. Using the percentage by mass, the mass of HCl in 1180 g of solution is (37.0/100) * 1180 g.
4. Step 4: Convert the mass of HCl to moles. Use the molar mass of HCl, which is approximately 36.46 g/mol, to convert the mass of HCl to moles.
5. Step 5: Calculate the molar concentration (molarity) of the solution. Molarity is defined as moles of solute per liter of solution. Use the moles of HCl calculated in Step 4 and divide by the volume of the solution in liters (1 L) to find the molarity.

Key Concepts

Mass Percent Concentration

Mass percent concentration is a way to express the concentration of a solution, defined as the mass of solute divided by the total mass of the solution, multiplied by 100. In this case, a 37.0% by mass HCl solution means that there are 37 grams of HCl in every 100 grams of the solution. Understanding this concept is crucial for converting mass to moles in the context of molarity.

Density and Volume Relationship

Density is defined as mass per unit volume, typically expressed in grams per milliliter (g/mL). The density of the hydrochloric acid solution is given as 1.18 g/mL, which allows us to calculate the volume of the solution based on its mass. This relationship is essential for determining how many liters of solution are present when calculating molarity.

Molarity Calculation

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. To find the molarity of the HCl solution, one must first convert the mass of HCl to moles using its molar mass, and then divide by the volume of the solution in liters. This concept is fundamental for solving the problem and determining the correct answer from the provided options.