Problem 72 - Chemistry The Molecular Nature of Matter

Question

In an aqueous solution of sulfuric acid, the concentration is \(1.89 \mathrm{~mol} \%\) of acid. The density of the solution is \(1.0645 \mathrm{~g} \mathrm{~mL}^{-1}\). Calculate the following: (a) the molal concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4},\) (b) the mass percent of the acid, and (c) the molarity of the solution.

Step-by-Step Solution

Answer

The molal concentration is approximately 103.66 mol/kg, the mass percent of acid is roughly 13.92%, and the molarity of the solution is about 17.74 M.

Step 1: Convert mol% to molality

Since mol% is given by the moles of solute per 100 moles of solution, and molality is moles of solute per kilogram of solvent, we need to assume a basis for calculation. Assume you have 100 moles of solution. You have 1.89 moles of sulfuric acid. The remaining 98.11 moles are presumably water. Convert the moles of water to mass (in kg) since the molality is measured in kg of solvent. The molar mass of water is approximately 18.015 g/mol. Calculate the mass of water and then the molality.

Step 2: Calculate the mass percent

Mass percent is given by the mass of the solute divided by the total mass of the solution multiplied by 100. From Step 1, you already have the mass of sulfuric acid and water. Add them to get the total solution mass, then divide the mass of sulfuric acid by the total mass, and multiply by 100 to get the mass percent.

Step 3: Calculate the molarity

To find the molarity, you need the number of moles of sulfuric acid and the volume of the solution in liters. Use the density given to convert the mass of the solution to volume. After finding the volume, divide the moles of sulfuric acid by the volume of the solution to get the molarity.

Key Concepts

Molality

Molality is a measure of the concentration of a solute in a solution, and it's represented as moles of solute per kilogram of solvent. It's particularly useful in scenarios involving temperature changes, as it remains constant since mass is not affected by temperature. To convert mol% to molality, you need to know the molar mass of both your solute and your solvent and calculate the mass of the solvent. It's important to correctly identify your solute and solvent; in the case of sulfuric acid in water, sulfuric acid is the solute and water is the solvent. Calculating molality requires careful consideration of the moles of each substance involved and their conversion to mass.

Mass Percent

The mass percent, also known as the weight percent, is an expression of the concentration of a component in a mixture. It is defined as the mass of the solute divided by the total mass of the solution, multiplied by 100 to get a percentage. This figure tells us how much of the solution's mass is made up by the solute. For solutions where the solute's mass and the total solution's mass are known, the mass percent can be easily calculated. It's imperative that all measurements are accurate and consistent, typically in grams, to ensure the calculation is valid. In practical applications, mass percent is often used in formulations to ensure proper amounts of substances are combined.

Molarity

Molarity is another common measure of concentration in chemistry. It represents the number of moles of solute per liter of solution. To find molarity, one must know the volume of the solution, which can be obtained from the mass and density, and the amount of solute in moles. It is a temperature-dependent measure since it involves volume, which can expand or contract with temperature changes. Molarity is commonly used for reactions taking place in the aqueous phase and it is important when preparing a solution to achieve a desired concentration for a chemical reaction or for quantitative analytical methods.

Aqueous Solution Chemistry

Aqueous solution chemistry deals with the reactions and properties of substances dissolved in water. Water is a remarkable solvent due to its polarity, and it's able to dissolve a wide range of substances, resulting in aqueous solutions. Understanding such solutions requires comprehension of concepts like solubility, electrolyte strength, and pH levels. In aqueous solutions, the interactions between water molecules and solute particles can affect both physical and chemical properties. Accurately measuring and calculating concentrations of substances in an aqueous solution is key for precise control of reaction conditions, which is crucial for any application ranging from industrial processing to laboratory research.