Problem 74 - General Chemistry

Question

What is the volume (in milliliters) of \(0.215 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) (sulfuric acid) containing \(0.949 \mathrm{~g} \mathrm{H}_{2} \mathrm{SO}_{4}\) ?

Step-by-Step Solution

Answer

45.0 mL

Step 1: Find Molar Mass of H₂SO₄

To find the molar mass of sulfuric acid (H₂SO₄), add the atomic masses of each element it contains. The elements are: 2 hydrogen (H), 1 sulfur (S), and 4 oxygen (O). From the periodic table: H = 1.01 g/mol, S = 32.07 g/mol, and O = 16.00 g/mol. Thus, the molar mass of H₂SO₄ is \(2(1.01) + 32.07 + 4(16.00) = 98.09\) g/mol.

Step 2: Calculate Moles of H₂SO₄

Using the mass given (0.949 g) and the molar mass of H₂SO₄ calculated in Step 1, calculate the number of moles using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). Therefore, \(\text{moles of H₂SO₄} = \frac{0.949}{98.09} \approx 0.00967\) moles.

Step 3: Use Molarity to Find Volume

Molarity (M) is defined as moles of solute per liter of solution. To find the volume in liters, use the formula: \(0.215 \, M = \frac{0.00967 \, \text{moles}}{\text{volume in liters}}\). Solve for volume: \(\text{volume in liters} = \frac{0.00967}{0.215}\approx 0.045\) L.

Step 4: Convert Volume to Milliliters

Convert the volume from liters to milliliters by using the conversion factor that 1 liter = 1000 milliliters. Therefore, \(0.045 \, \text{L} = 0.045 \times 1000 = 45.0\) mL.

Key Concepts

Molar Mass

Molar mass is a fundamental concept in the world of chemistry, especially useful in stoichiometry and calculations involving chemicals. To find the molar mass of a compound like sulfuric acid (H₂SO₄), you need to add up the atomic masses of each element in the compound. For H₂SO₄, it consists of 2 hydrogen atoms, 1 sulfur atom, and 4 oxygen atoms. By using the periodic table, we find that hydrogen has an atomic mass of approximately 1.01 g/mol, sulfur has 32.07 g/mol, and oxygen has 16.00 g/mol. In this specific case: - Hydrogen: 2 atoms × 1.01 g/mol = 2.02 g/mol - Sulfur: 1 atom × 32.07 g/mol = 32.07 g/mol - Oxygen: 4 atoms × 16.00 g/mol = 64.00 g/mol Summing these, the molar mass of H₂SO₄ is 98.09 g/mol. Understanding molar mass is crucial for converting between mass and moles, essential for chemical calculations.

Molarity

Molarity is a measure of the concentration of a solute in a solution, given in moles per liter (mol/L). It tells us how much solute is present in a certain volume of the solution. For instance, a 0.215 M sulfuric acid solution means there are 0.215 moles of H₂SO₄ per liter of solution. This unit helps us relate the amount of solute (in moles) to the volume of the entire solution.To calculate the volume of a solution required to contain a specified amount of solute, you can rearrange the formula for molarity:\[M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]If you know the moles of solute and the molarity, you can solve for the volume by rearranging: \[\text{Volume} = \frac{\text{moles}}{\text{molarity}}\]This concept is widely applied in laboratory settings and industries where precise concentrations are crucial.

Sulfuric Acid

Sulfuric acid (H₂SO₄) is one of the most important industrial chemicals, extensively used in the production of fertilizers, chemicals, and in petroleum refining. It is a diprotic acid, meaning it can donate two protons (H⁺ ions) in a reaction, making it a strong acid. This property is particularly important when neutralizing bases or participating in various reactions. Due to its strength and reactive nature, sulfuric acid must be handled with care. It can cause severe chemical burns upon contact with skin and should always be concentrated in controlled environments. Its role in chemical calculations often involves determining its concentration in a solution, as illustrated in stoichiometry problems like the one given. An important point to remember is that its formulation and concentration in a solution directly influence its properties and potential hazards.

Chemical Calculations

Chemical calculations are essential tools for predicting and understanding the outcomes of chemical reactions. They frequently rely on concepts such as molar mass, molarity, and balanced chemical equations. Let's break this down further:- Using molar mass, you can convert between mass and moles. This conversion aids in relating the real-world quantity of a substance to a standardized amount based on Avogadro's number (6.022 × 10²³ entities per mole).- Molarity allows you to determine the concentration of solutions, which is critical for reactions occurring in solutions.Consider the original problem: determining the volume of 0.215 M sulfuric acid that contains 0.949 grams of the acid. Using the known molar mass (98.09 g/mol), you convert grams to moles. Then, knowing the molarity, calculate how much volume is needed to achieve that concentration:\[\text{moles of H₂SO₄} = \frac{0.949 \, \text{g}}{98.09 \, \text{g/mol}} = 0.00967 \, \text{moles}\]Finally, solve for volume:\[\text{Volume in liters} = \frac{0.00967}{0.215} \approx 0.045 \, \text{L} = 45.0 \, \text{mL}\]Mastering these calculations empowers you to handle complex reactions and solution preparations confidently.