Question

Calculate the normality of a solution containing \(2.45 \mathrm{~g}\) of sulfuric acid in \(2.00\) liters of solution. (MW of \(\mathrm{H}_{2} \mathrm{SO}_{4}=98.1\).)

Short answer

Normality (N) = \(\frac{\frac{2.45 \ \mathrm{g}}{98.1 \ \mathrm{g/mol}} \times 2}{2.00 \ \mathrm{L}} = 0.0500 \ \mathrm{N}\) The normality of the solution containing $2.45 \mathrm{~g}$ of sulfuric acid in $2.00$ liters of solution is \(0.0500 \ \mathrm{N}\).

Step-by-step solution

Determine the number of equivalents of H₂SO₄ present in the solution

To find the number of equivalents, we first need to find the number of moles of H₂SO₄ present. We can do this by dividing the mass of H₂SO₄ by its molecular weight (MW). Moles of H₂SO₄ = \(\frac{2.45 \ \mathrm{g}}{98.1 \ \mathrm{g/mol}}\) Now, let's calculate the number of equivalents by considering the number of acidic protons in H₂SO₄. Since H₂SO₄ has 2 acidic protons (H⁺), we multiply the number of moles by 2 to get the number of equivalents: Equivalents of H₂SO₄ = Moles of H₂SO₄ × 2

Calculate the volume of the solution in liters

The volume of the solution is given as 2.00 liters, so there is no need to convert it.

Calculate the normality of the solution

Now, we can calculate the normality of the solution by dividing the number of equivalents of H₂SO₄ by the volume of the solution in liters: Normality (N) = \(\frac{\text{Equivalents of H₂SO₄}}{\text{Volume of solution in liters}}\) Now substituting the values we calculated in step 1 and step 2, we get: Normality (N) = \(\frac{\frac{2.45 \ \mathrm{g}}{98.1 \ \mathrm{g/mol}} \times 2}{2.00 \ \mathrm{L}}\) By calculating the above expression, we will get the normality of the solution.

Key concepts

Sulfuric acid equivalents

Understanding sulfuric acid equivalents is essential when calculating the normality of a solution. Sulfuric acid, H₂SO₄, is a strong acid that can donate two protons (H⁺ ions) when it dissolves in water. This means it has two equivalents per mole. To determine the number of equivalents in a given solution, we first calculate the moles of H₂SO₄ using its mass and molecular weight. Once the moles are known, the equivalence factor comes into play. By multiplying the number of moles by the number of protons sulfuric acid can donate (which is 2), we get the total number of equivalents. This factor is crucial for understanding how sulfuric acid behaves in different chemical reactions, especially in acid-base titrations.

Molecular weight calculation

The molecular weight (or molar mass) of a substance is a key term in chemistry. For sulfuric acid, H₂SO₄, its molecular weight is given as 98.1 g/mol. To calculate this, we add up the atomic masses of all the atoms in the molecular formula:

• Hydrogen (H): 2 atoms × 1.01 g/mol = 2.02 g/mol
• Sulfur (S): 1 atom × 32.07 g/mol = 32.07 g/mol
• Oxygen (O): 4 atoms × 16.00 g/mol = 64.00 g/mol

Summing these values gives us the molecular weight of sulfuric acid: 98.1 g/mol. This is a fundamental value because it allows us to convert between grams and moles, which is necessary for various calculations, including those involving solution concentrations.

Acidic protons in sulfuric acid

Sulfuric acid is considered a diprotic acid because it has two acidic protons that it can donate. When it dissolves in water, it dissociates in two steps:

• The first proton dissociates completely, making sulfuric acid a strong acid.
• The second dissociation is also significant, though not as complete as the first.

Acknowledging these two protons is vital for calculating equivalents and thus the normality of sulfuric acid solutions. This characteristic enables sulfuric acid to play a critical role in many industrial and laboratory processes due to its strong acidic nature.

Solution volume in liters

Solution volume is a basic yet vital aspect when determining concentration measures like normality or molarity. In this problem, the volume of the sulfuric acid solution is given as 2.00 liters, which is already in the desired unit for the normality calculation. Volume in liters is used because it simplifies the concept of concentration, making it possible to directly divide the number of equivalents or moles by the volume. This conversion to liters is important because the metric system is universally used in scientific calculations, providing a standardized way to report measurement results and foster easy comparison between different datasets.