Problem 69 - Introductory Chemistry Atoms First

Question

Consider sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), used in car batteries. (a) What is the molar mass of sulfuric acid? (b) What is the mass in grams of 1 mole of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\) (c) What is the mass in grams of \(2.50\) moles of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\) (d) What is the mass in grams of 1000 molecules of \(\mathrm{H}_{2} \mathrm{SO}_{4} ?\) (Hint: Start by writing \({ }^{\prime \prime} 1000\) molecules \(\mathrm{H}_{2} \mathrm{SO}_{4}^{\prime \prime}\) and then apply conversior factors. Remember our admonition: If in doubt, convert to moles.)

Step-by-Step Solution

Answer

The molar mass of sulfuric acid (H₂SO₄) is 98 g/mol. The mass of 1 mole of H₂SO₄ is 98 g, and the mass of 2.5 moles is 245 g. The mass of 1000 molecules of H₂SO₄ is approximately \(1.63 \times 10^{-19}\) g.

Step 1: Find the molar mass of sulfuric acid (H₂SO₄)

To find the molar mass of H₂SO₄, we need to first identify the atomic masses of hydrogen (H), sulfur (S), and oxygen (O) using the periodic table. The atomic masses are approximately: - Hydrogen (H): 1 g/mol - Sulfur (S): 32 g/mol - Oxygen (O): 16 g/mol Now we can calculate the molar mass of H₂SO₄ as follows: Molar mass of H₂SO₄ = (2 × atomic mass of H) + (1 × atomic mass of S) + (4 × atomic mass of O)

Step 2: Calculate the molar mass of H₂SO₄

Use the atomic masses found in Step 1 to calculate the molar mass of H₂SO₄: Molar mass of H₂SO₄ = (2 × 1 g/mol) + (1 × 32 g/mol) + (4 × 16 g/mol) \(=\) 2 g/mol + 32 g/mol + 64 g/mol \(=\) 98 g/mol The molar mass of H₂SO₄ is 98 g/mol.

Step 3: Calculate the mass of 1 mole and 2.5 moles of H₂SO₄

We can use the molar mass calculated in Step 2 to find the mass of 1 mole and 2.5 moles of H₂SO₄. a) For 1 mole of H₂SO₄: Mass = (molar mass) × (number of moles) Mass = 98 g/mol × 1 mol = 98 g b) For 2.5 moles of H₂SO₄: Mass = (molar mass) × (number of moles) Mass = 98 g/mol × 2.5 mol = 245 g

Step 4: Calculate the mass of 1000 molecules of H₂SO₄

To calculate the mass of 1000 molecules of H₂SO₄, we first need to convert the number of molecules to moles: Number of moles = (number of molecules) / (Avogadro's number) Number of moles = 1000 molecules / \(6.022 \times 10^{23}\) molecules/mol = \(1.66 \times 10^{-21}\) mol Now we can use the molar mass to find the mass: Mass = (molar mass) × (number of moles) Mass = 98 g/mol × \(1.66 \times 10^{-21}\) mol ≈ \(1.63 \times 10^{-19}\) g So, the mass of 1000 molecules of H₂SO₄ is approximately \(1.63 \times 10^{-19}\) g.

Key Concepts

Understanding Molar Mass

The molar mass is an essential concept in chemistry that represents the mass of one mole, or around 6.022 x 10^23 particles (a number known as Avogadro's number), of a given substance. This mass is expressed in grams per mole (g/mol) and can be calculated by summing the atomic masses of all atoms in a molecule. For sulfuric acid, which has the formula \(\mathrm{H}_{2}\mathrm{SO}_{4}\), you need to know the atomic masses of its elements:

• Hydrogen (H): 1 g/mol
• Sulfur (S): 32 g/mol
• Oxygen (O): 16 g/mol

By adding these values, you calculate the molar mass. With two hydrogen atoms, one sulfur atom, and four oxygen atoms, the total molar mass sums to 98 g/mol. Understanding molar mass helps in determining the mass of substances when the amount in moles is given.

Calculating Molecular Weight

Molecular weight, often interchangeable with molar mass in practical use, is the sum of the atomic masses of atoms present in a molecule, expressed in atomic mass units (amu). Each atom's contribution is scaled by frequency in the molecule. For instance, in \(\mathrm{H}_{2}\mathrm{SO}_{4}\), you multiply the atomic mass of each element by its number of atoms:

• 2 Hydrogens: \(2 \times 1 = 2 \text{ amu}\)
• 1 Sulfur: \(1 \times 32 = 32 \text{ amu}\)
• 4 Oxygens: \(4 \times 16 = 64 \text{ amu}\)

This results in a total of 98 amu for sulfuric acid. This calculation is vital for understanding and working with chemical reactions, especially in balancing equations and converting between moles and grams.

Exploring Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is a fundamental constant that defines the number of atoms, molecules, or particles in a mole of substance. Its immense value makes it a powerful link between microscale molecular structures and macroscale grams. In practical terms, using Avogadro's number allows conversion from molecules to moles, an essential step in performing many chemical calculations. For example, if you have 1000 molecules of \(\mathrm{H}_{2}\mathrm{SO}_{4}\), you divide by Avogadro's number to convert that quantity into an amount in moles: \[ \text{Number of moles} = \frac{1000}{6.022 \times 10^{23}} \approx 1.66 \times 10^{-21} \text{ moles} \]This conversion is key for accurate mass calculations in chemical experiments.

Practical Chemical Calculations

Chemical calculations allow chemists to determine quantities like mass, mole numbers, and concentrations in reaction equations. For example, if calculating the mass of a compound like sulfuric acid, use the formula:

• Mass = (Molar Mass) x (Number of Moles)

For one mole of \(\mathrm{H}_{2}\mathrm{SO}_{4}\), calculate mass as:\[ 98 \text{ g/mol} \times 1 \text{ mol} = 98 \text{ g} \]For multiple moles, simply scale the calculation:\[ 98 \text{ g/mol} \times 2.5 \text{ mol} = 245 \text{ g} \]This approach extends to finding the mass of a specific number of molecules, where you'll first convert molecules to moles, then to mass, through noted formulas. Such calculations aid in predicting reaction progression and substances needed or produced.