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 approximately \(193.70\, \text{mol/kg}\); molarity is \(17.82\, \text{mol/L}\).

Step 1: Calculate the Mass of Solvent

The density of sulfuric acid is given as \(1.84\, \mathrm{g/cm^3}\) and the solution is \(95.0\%\) by weight \(\mathrm{H_2SO_4}\). Assume \(1\, \text{L}\) of solution, which has a mass of \(1840\, \text{g}\). The mass of \(\mathrm{H_2SO_4}\) is \(0.95 \times 1840\, \text{g} = 1748\, \text{g}\). The mass of water is \(1840\, \text{g} - 1748\, \text{g} = 92\, \text{g}\).

Step 2: Convert Mass of Solvent to Kilograms

Convert the mass of water from grams to kilograms for the molality calculation. \(92\, \text{g} = 0.092\, \text{kg}\).

Step 3: Calculate Moles of Sulfuric Acid

The molar mass of \(\mathrm{H_2SO_4}\) is \(98.09\, \mathrm{g/mol}\). Calculate the moles: \(\frac{1748\, \text{g}}{98.09\, \text{g/mol}} \approx 17.82\, \text{mol}\).

Step 4: Calculate Molality

Molality (\(b\)) is defined as moles of solute per kilogram of solvent. \(b = \frac{17.82\, \text{mol}}{0.092\, \text{kg}} \approx 193.70\, \text{mol/kg}\).

Step 5: Calculate Molarity

The volume of solution is \(1\, \text{L}\). Molarity (\(M\)) is defined as moles of solute per liter of solution. \(M = \frac{17.82\, \text{mol}}{1\, \text{L}} = 17.82\, \text{mol/L}\).

Key Concepts

Density

Density is a measure of how much mass is contained in a given volume. It is often expressed in grams per cubic centimeter (g/cm³) or kilograms per liter (kg/L). For chemical solutions, knowing the density helps to relate the mass of the solution to its volume.
For example, the density of concentrated sulfuric acid is given as 1.84 g/cm³.
This means that each cubic centimeter of the solution weighs 1.84 grams.

• To calculate the mass of a particular volume of the solution, multiply the volume by the density.
• In this exercise, assuming 1 L of solution, which is 1000 cm³, the mass would be 1.84 g/cm³ x 1000 cm³ = 1840 g.

Understanding density is crucial for determining how concentrated a solution is on a mass basis.

Molality

Molality is a way of expressing the concentration of a solution in terms of the amount of solute present in a given mass of solvent. It is expressed in moles of solute per kilogram of solvent.
This unit is particularly useful in certain chemical calculations where temperature variations affect the volume but not the mass of the solution.

• To calculate molality, divide the number of moles of solute by the mass of the solvent in kilograms.
• In our example, 17.82 moles of \(\mathrm{H_2SO_4}\) are dissolved in 0.092 kg of water, yielding a molality of approximately 193.70 mol/kg.

Molality is different from molarity which is based on the volume of the whole solution.

Molarity

Molarity is another common way of expressing solution concentration, representing the number of moles of solute per liter of solution. It is denoted as mol/L or simply M. Molarity changes with temperature, as temperature affects the volume of the solution, unlike molality.
To calculate, divide the number of moles of solute by the total volume of the solution in liters.

• In this problem, 17.82 moles of sulfuric acid were in a 1 L solution, making the molarity 17.82 M.

This concept is particularly useful in stoichiometric calculations for chemical reactions in solutions where precise volumes are measured.

Molar Mass

Molar mass is a property that tells you the weight of one mole of a particular substance. It is expressed in grams per mole (g/mol) and is specific to each chemical compound, calculated from atomic masses found on the periodic table.
For sulfuric acid \(\mathrm{H_2SO_4}\), the molar mass is calculated as:

• 2 hydrogen atoms = 2 \(\times 1.01\) g/mol
• 1 sulfur atom = 32.07 g/mol
• 4 oxygen atoms = 4 \(\times 16.00\) g/mol

Adding these together gives 98.09 g/mol as the molar mass for \(\mathrm{H_2SO_4}\). It is a useful concept for converting between moles and grams.

Solution Concentration

Solution concentration is a general term that refers to how much solute is in a given amount of solvent or solution. It can be expressed in various ways, including molarity and molality. Each type serves different purposes depending on the context of the experiment or calculation.
In the context of the given problem, both the molarity (17.82 M) and molality (193.70 mol/kg) are used to express the concentration of sulfuric acid.

• Molarity is useful for reactions that take place in solution and require volumetric analysis.
• Molality is more appropriate for situations where independent of volume changes, such as in colligative property calculations.

Understanding these concepts is essential for solving real-world problems in chemistry where solution concentration needs to be accurately described.