Problem 10 - Chemistry and Chemical Reactivity

Question

Concentrated sulfuric acid has a density of \(1.84 \mathrm{g} /\) \(\mathrm{cm}^{3}\) and is \(95.0 \%\) by weight \(\mathrm{H}_{2} \mathrm{SO}_{4} .\) What is the molality of this acid? What is its molarity?

Step-by-Step Solution

Answer

Molality is 193.5 mol/kg; Molarity is 17.8 mol/L.

Step 1: Understand the Problem

We need to find both the molality and the molarity of the acid. Molality is measured in moles of solute per kilogram of solvent, while molarity is measured in moles of solute per liter of solution.

Step 2: Determine Molar Mass of Sulfuric Acid

Calculate the molar mass of sulfuric acid (H₂SO₄). The molar mass for H is 1 g/mol, S is 32 g/mol, and O is 16 g/mol. Thus, the molar mass is: \(2 \times 1 + 32 + 4 \times 16 = 98 \text{ g/mol}\).

Step 3: Calculate Mass of Solution

Assume we have 1 liter (1000 cm³) of sulfuric acid solution. The mass of this solution is density \(\times\) volume: \(1.84 \text{ g/cm}^3 \times 1000 \text{ cm}^3 = 1840 \text{ g}\).

Step 4: Calculate Mass of Sulfuric Acid

Given that the solution is 95% by weight sulfuric acid, the mass of H₂SO₄ is \(0.95 \times 1840 \text{ g} = 1748 \text{ g}\).

Step 5: Calculate Moles of Sulfuric Acid

Using the molar mass, calculate moles of sulfuric acid: \(\frac{1748 \text{ g}}{98 \text{ g/mol}} = 17.8 \text{ mol}\).

Step 6: Calculate Mass of Solvent

Subtract the mass of sulfuric acid from the total solution mass to find the mass of the solvent (water): \(1840 \text{ g} - 1748 \text{ g} = 92 \text{ g}\), or \(0.092 \text{ kg}\).

Step 7: Calculate Molality

Molality is moles of solute per kilogram of solvent: \( \frac{17.8 \text{ mol}}{0.092 \text{ kg}} = 193.5 \text{ mol/kg}\).

Step 8: Calculate Molarity

Molarity is moles of solute per liter of solution. Since we assume 1 liter, the molarity is simply \(17.8 \text{ mol/L}\).

Key Concepts

Molality

Molality is a concentration term that is particularly useful in scenarios where temperature might change since it remains unaffected by temperature variations. It measures the number of moles of solute, in this case, sulfuric acid, per kilogram of solvent, which is water here. To calculate molality, remember the following steps:

• First, determine the mass of the solute, which is the sulfuric acid, and the mass of the solvent, which is water alone.
• Calculate the molar mass of the solute to convert its mass into moles.
• Then, subtract the mass of the solute from the total mass of the solution to get the mass of the solvent.
• Finally, divide the number of moles of solute by the mass of the solvent in kilograms to get molality.

In our exercise, you can see that once we determined the necessary values, the molality was found to be 193.5 mol/kg, showing quite a high concentration in relation to the solvent. Molality is essential in colligative property calculations like boiling point elevation and freezing point depression.

Molarity

Molarity is another way to express the concentration of a solute, but unlike molality, it accounts for the volume of the solution. As a result, it changes with temperature since the volume of liquids can expand or contract with temperature fluctuations. To find molarity:

• Calculate the number of moles of the solute, using its molar mass.
• Measure or compute the volume of the entire solution in liters.
• Divide the moles of solute by the volume of the solution in liters to find molarity.

For our sulfuric acid example, we assumed a 1-liter solution volume, which simplifies the molarity calculation to merely use the moles of the solute. This is why the molarity here is straightforwardly 17.8 mol/L. Though molarity is sensitive to temperature, it is widely used due to its direct relation with solution volumes, making it practical for lab settings.

Chemical Calculations

Chemical calculations are foundational to understanding reactions, concentrations, and various properties in chemistry. They help us convert real-life measurements and data into meaningful chemical insight. Let's consider the calculations involved in our example.

• Start by knowing the specific density of the solution, which allows calculation of mass for a given volume.
• Next, determine the mass percentages, as they help you identify the individual component weights in mixtures, such as the pure sulfuric acid and the solvent in this case.
• Utilize the molar mass of chemicals to transition from mass to moles, a crucial step for both molality and molarity.
• Temperature, pressure, density, and phase of matter are crucial physical factors often involved in these calculations.

Breaking down these complex steps provides vital insights not only into the composition of solutions like sulfuric acid but also into more advanced applications involving reaction stoichiometry and kinetics. Emphasizing practice with these calculations strengthens your chemistry skills, paving the way for more accurate experiments and analyses.