Problem 83 - Chemistry Matter and Change

Question

What are the molality and mole fraction of solute in a 35.5 percent by mass aqueous solution of formic acid \((\mathrm{HCOOH}) ?\)

Step-by-Step Solution

Answer

The molality of formic acid in the 35.5% by mass aqueous solution is \(11.95 \, mol/kg\), and the mole fraction of formic acid is 0.177.

Step 1: Determine the mass of solute and solvent

Assuming 100 g of solution, the mass of solute (formic acid) is 35.5 g (35.5% of 100 g) and the mass of solvent (water) is 100g - 35.5 g = 64.5 g.

Step 2: Calculate moles of solute and solvent

To calculate the moles of solute and solvent, we use the molar mass of formic acid and water. The molar mass of formic acid (HCOOH) is: \(1 \times\)(H) + \(1 \times\)(C) + \(2 \times\)(O) + \(1 \times\)(H) = \(1 + 12 + 32 + 1 = 46 g/mol\). The molar mass of water (H₂O) is: \(2 \times\) (H) + \(1 \times\)(O) = \(2+ 16 = 18 g/mol\). Now, we can find the moles of each substance: Moles of formic acid: \[\frac{35.5 \, g}{46 \, g/mol} = 0.771 \, mol\] Moles of water: \[\frac{64.5 \, g}{18 \, g/mol} = 3.58 \, mol\]

Step 3: Calculate the molality of formic acid

Molality is defined as the moles of solute per kilogram of solvent. We already have the values for the moles of formic acid and the mass of water. Now, we need to convert the mass of water from grams to kilograms: Mass of water in kilograms: \[\frac{64.5 \, g}{1000 \, g/kg} = 0.0645 \, kg\] Now, we can find the molality of formic acid: Molality (m) = \(\frac{moles \, of \, solute}{mass \, of \, solvent \, (kg)}\) \( m = \frac{0.771 \, mol }{0.0645 \, kg} = 11.95 \, mol/kg\)

Step 4: Calculate the mole fraction of formic acid

Mole fraction is the ratio of the moles of one component to the total moles of all components in the solution. In this case, we need to find the ratio of moles of formic acid to the total moles of formic acid and water: Mole fraction (X) = \(\frac{moles \, of \, formic \,acid}{moles \, of \, formic \, acid + moles \, of \, water}\) \( X = \frac{0.771 \, mol}{0.771 \, mol + 3.58 \, mol} = 0.177\) So, the molality of formic acid in the solution is \(11.95 \, mol/kg\), and the mole fraction of formic acid is 0.177.

Key Concepts

Mole Fraction

The mole fraction is a way to express the concentration of a component in a mixture. It's important because it gives a simple ratio of moles, which can be used in chemical calculations. The mole fraction of a component is defined as the number of moles of that component divided by the total number of moles of all substances in the solution.

To calculate the mole fraction, you'll follow these steps:

• Find the number of moles of each substance using their masses and molar masses.
• Add together the numbers of moles to get the total moles in the solution.
• Divide the moles of the desired component by the total moles.

For example, in a solution of formic acid and water, you would calculate the moles of both and then divide the moles of formic acid by the total moles to find its mole fraction.

Formic Acid

Formic acid is a simple carboxylic acid with the chemical formula HCOOH. It's known for being the acidic component of ant stings. In chemistry, formic acid is used for different purposes such as in the manufacture of leather and textiles.

When working with formic acid in solutions, it is crucial to understand its properties, including its molar mass, which is 46 g/mol. This allows chemists to easily convert between mass and moles when determining concentrations. Formic acid can participate in hydrogen bonding, making it an interesting compound to study in aqueous solutions.

Aqueous Solution

An aqueous solution is a solution where water is the solvent. Water, known as the 'universal solvent,' can dissolve many substances due to its polar nature. When formic acid is added to water, it forms an aqueous solution.

In aqueous solutions, it's important to distinguish between solute and solvent:

• The solute is the substance dissolved (e.g., formic acid).
• The solvent is the substance doing the dissolving (in this case, water).

Understanding this helps in calculations involving molality and mole fractions, as these values depend heavily on identifying the roles of different substances in the solution. In our example, the mass of water and formic acid must be known to find the molality and mole fraction accurately.

Mass Percent

Mass percent is a way to describe the composition of a mixture. It tells you what percentage of the total mass of the solution comes from a specific component.

The formula for mass percent is:\[\text{Mass Percent} = \left(\frac{\text{mass of solute}}{\text{mass of solution}}\right) \times 100\%\]For example, in a solution with 35.5 g of formic acid in 100 g of solution, the mass percent of formic acid is 35.5%. This percentage helps chemists and students understand what fraction of the solution is made up of the solute, influencing properties like boiling and freezing points. Mass percent is also crucial for conversions needed to find other concentrations, such as molality.