Question

How would you prepare \(5.00 \mathrm{~L}\) of a solution that is \(43.0 \% \mathrm{H}_{2} \mathrm{SO}_{4}\) by mass if the resulting solution has a density of \(1.329 \mathrm{~g} / \mathrm{mL} ?\) What is the molarity of the resulting solution?

Short answer

Question: Calculate the molarity of a solution made by preparing 5.00 L of a solution that is 43.0% H2SO4 by mass, with a density of 1.329 g/mL. Answer: The molarity of the resulting solution is 5.82 M.

Step-by-step solution

Determine the mass of the solution

First, we need to find out how heavy the 5.00 L of solution is. We can do this using the density of the solution which is given as 1.329 g/mL. Since 1 L = 1000 mL, we can convert the volume to mL: Volume = \((5.00 \mathrm{~L}) \times (1000 \mathrm{~mL} / \mathrm{L}) = 5000 \mathrm{~mL}\) Now, we can calculate the mass of the solution using the density formula: Mass = Density × Volume = \((1.329 \mathrm{~g/ mL}) \times (5000 \mathrm{~mL}) = 6645 \mathrm{~g}\)

Calculate the mass of H2SO4 and mass of the solvent in the solution

Since the solution is 43.0% H2SO4 by mass, this means that for every 100 g of the solution, 43 grams are H2SO4 and the remaining 57 grams are the solvent. So we can find the mass of H2SO4 and the mass of the solvent in the solution: Mass of H2SO4 = \((0.430) \times (6645 \mathrm{~g}) = 2855.35 \mathrm{~g}\) Mass of solvents = \(6645 \mathrm{~g} - 2855.35 \mathrm{~g} = 3789.65 \mathrm{~g}\)

Calculate the moles of H2SO4 in the solution

To determine the number of moles of H2SO4 in the solution, we will use the molar mass of H2SO4. The molar mass of H2SO4 is approximately 98.08 g/mol. Moles of H2SO4 = \(\frac{2855.35 \mathrm{~g}}{98.08 \mathrm{~g/mol}} = 29.09 \mathrm{~mol}\)

Calculate the molarity of the H2SO4 solution

Finally, we can now calculate the molarity of the H2SO4 solution using the Moles of H2SO4 and the volume of the solution. Molarity = \(\frac{29.09 \mathrm{~mol}}{5.00 \mathrm{~L}} = 5.82 \mathrm{M}\) The molarity of the resulting solution is 5.82 M.

Key concepts

Solution Concentration

When working in chemistry, understanding the concentration of solutions is crucial. Concentration refers to the amount of a substance, known as the solute, that is contained within a certain volume of solvent. It indicates how 'strong' or 'weak' a solution is and plays a pivotal role in reactions and experiments. The term can be expressed in various ways, including molarity, molality, normality, and mass percent.

In the example provided, the mass percent concentration is especially important. It is given that the sulfuric acid solution has a mass percent of 43.0%, which means that in every 100 grams of the solution, there will be 43 grams of sulfuric acid. This type of concentration is particularly useful when dealing with the physical properties of the solution, such as density, boiling point, and so on.

Molarity Calculation

Molarity is one of the most common units for expressing the concentration of a solution. It is defined as the number of moles of solute per liter of solution. Calculating molarity requires knowing the volume of the solution and the amount of solute in moles. The formula is written as:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \].

To demonstrate molarity calculation using the given exercise, we first calculated the moles of sulfuric acid before dividing it by the volume of the solution in liters. This resulted in a molarity of 5.82 M. Having a strong grasp of molarity allows students to predict the outcomes of reactions and to prepare solutions of precise strengths for lab experiments.

Mass Percent Composition

Mass percent composition is another method of expressing solution concentration, which shows the mass of the solute as a percentage of the total mass of the solution. It is calculated using the formula:
\[ \text{Mass percent} = \frac{\text{mass of solute}}{\text{total mass of solution}} \times 100\% \].

In the context of the provided example, to find the mass of sulfuric acid (\(H_2SO_4\)), the mass percent value of 43.0% was multiplied by the total mass of the solution. Understanding the mass percent composition assists in preparing solutions where the precise mass of solute and solvent has to be measured. It is particularly relevant when we are dealing with reactions involving solids or when the conservation of mass is critical.

Solution Density

The density of a solution is a physical property that relates its mass to its volume, usually expressed in grams per milliliter (g/mL) or grams per liter (g/L). It can be used to determine the mass of a solution, given its volume, or vice versa. The formula for density is simple:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \].

In our problem, the density was a pivotal piece of information used to first find the mass of the entire sulfuric acid solution. With a known volume of 5.00 L and a density of 1.329 g/mL, we calculated a total mass of the solution, which then enabled us to determine the respective masses of the solute and the solvent. Understanding solution density helps in many aspects of chemistry, from characterizing substances to designing experimental protocols.