Problem 16 - General Chemistry: Principles and Modern Applications

Question

6.00 M sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) has a density of \(1.338 \mathrm{g} / \mathrm{mL} .\) What is the percent by mass of sulfuric acid in this solution?

Step-by-Step Solution

Answer

The percent by mass of sulfuric acid in this solution is 43.9%.

Step 1: Calculate mass of the solute (sulfuric acid)

The molarity of a solution is defined as the number of moles of solute per liter of solution. Therefore, one liter of this 6.00 M sulfuric acid solution contains \(6.00 \times Molar mass of H_{2}SO_{4}\) grams of sulfuric acid. Molar mass of \(H_{2}SO_{4} = (2\times1.0) + 32.0 + (4\times16.0) = 98\,g/mol\), so there are \(6.00 mol/L \times 98\,g/mol = 588\,g\) of \(H_{2}SO_{4}\) in one liter of solution.

Step 2: Calculate the mass of the solvent (water)

The density of the solution is given as 1.338 g/mL. So, the mass of 1 liter of solution (1 L=1000 mL): In grams, this will be \(1.338 g/mL \times 1000 mL = 1338 g\). We previously calculated that 1 L of solution contains 588 g of the solute. Therefore, the mass of water in one liter of solution will be \( 1338 g - 588 g = 750 g\).

Step 3: Calculate percent by mass of sulfuric acid

The percent by mass is given by the mass of the solute divided by the total mass of the solution, times 100. Therefore, \% by mass = \(\frac{Mass_{solute}}{Mass_{solvent} + Mass_{solute}} \times 100%\). Plugging in the values obtained, we find \% by mass = \(\frac{588\,g}{750\,g + 588\,g} \times 100 = 43.9%\). The sulfuric acid solution has a mass/mass percent concentration of 43.9%.

Key Concepts

Percent by Mass

When working with chemical solutions, percent by mass is a common way to express concentration. It tells you the ratio of the mass of the solute to the total mass of the solution, which includes both the solute and the solvent. This is particularly helpful in understanding how much of a chemical substance is actually present in a given amount of solution.

To calculate percent by mass, you use the formula:

• \[ \text{Percent by Mass} = \left( \frac{\text{Mass of Solute}}{\text{Mass of Solute} + \text{Mass of Solvent}} \right) \times 100\% \]

For the sulfuric acid solution given, this calculation involves identifying both the mass of the solute (sulfuric acid) and the mass of the solvent (water) in one liter of solution.

Molarity

Molarity is a key concept in chemistry defined as the number of moles of a solute per liter of solution. It provides insight into the concentration of a substance in a liquid and is often denoted by the symbol \(M\). Understanding molarity is essential for preparing solutions in laboratory settings and for conducting experiments that require precise chemical reactions.

The formula for molarity is:

• \[ M = \frac{\text{Moles of Solute}}{\text{Liters of Solution}} \]

In the example of sulfuric acid, a 6.00 M solution means there are 6 moles of sulfuric acid dissolved in every liter of water. Calculations with molarity are crucial in determining the exact amounts of chemicals needed for reactions.

Density Calculations

Density is a measure of how much mass is contained in a given volume. In chemistry, it is expressed in units such as grams per milliliter (g/mL) and is used to convert between the volume and mass of a substance. This is particularly useful when working with solutions, as it allows us to understand and predict how they will behave in different scenarios.

The density of a substance is calculated using the formula:

• \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

For the sulfuric acid solution with a density of 1.338 g/mL, it translates to mass calculations useful in determining mass-related properties of the solution when volume is known.

Sulfuric Acid

Sulfuric acid, represented as \(\mathrm{H}_{2}\mathrm{SO}_{4}\), is a strong acid widely used in industrial and chemical processes. Its properties make it essential for applications ranging from fertilizer production to battery acid and chemical synthesis.

Understanding its concentration in solutions, like the 6.00 M solution discussed, requires the knowledge of its molar mass, which is 98 g/mol. This information helps calculate how much sulfuric acid is present, making it critical to safely and effectively use in experiments. It is known for its dehydrating and exothermic properties, which means it can release heat when mixed with water. Always handle with care and be sure to use appropriate safety measures.