Question

molecular masses
calculate the molecular mass (in amu’s) for these molecules: (use atomic masses to at least two decimal places)
nano₃ amu
cl₂ amu
ca(oh)₂ amu
hc₂h₃o₂ amu
co₂ amu
n₂o amu
naocl amu
ca(no₃)₂ amu
ch₃oh amu
h₂so₄ amu
caso₄ amu
cacl₂ amu

Answer:

To solve for the molecular mass of each compound, we use the atomic masses (in amu) of the constituent elements: \( \text{Na} = 22.99 \), \( \text{N} = 14.01 \), \( \text{O} = 16.00 \), \( \text{Cl} = 35.45 \), \( \text{Ca} = 40.08 \), \( \text{H} = 1.01 \), \( \text{C} = 12.01 \), \( \text{S} = 32.07 \), \( \text{K} = 39.10 \) (if needed), etc. We calculate the sum of the atomic masses of all atoms in the molecule. Here are the calculations for a few examples (we'll do \( \text{NaNO}_3 \), \( \text{Cl}_2 \), and \( \text{Ca(OH)}_2 \) as samples; the rest follow the same method):

1. \( \text{NaNO}_3 \)

Step 1: Identify atoms and their counts

• \( \text{Na} \): 1 atom
• \( \text{N} \): 1 atom
• \( \text{O} \): 3 atoms

Step 2: Multiply each atomic mass by its count

• \( \text{Na} \): \( 1 \times 22.99 = 22.99 \)
• \( \text{N} \): \( 1 \times 14.01 = 14.01 \)
• \( \text{O} \): \( 3 \times 16.00 = 48.00 \)

Step 3: Sum the masses

\( 22.99 + 14.01 + 48.00 = 85.00 \) amu (wait, actually, more precisely: \( 22.9898 + 14.0067 + 3 \times 15.9994 \approx 22.9898 + 14.0067 + 47.9982 = 84.9947 \approx 84.99 \) amu if we use more precise atomic masses, but often rounded values are used. Let's use \( \text{Na} = 22.99 \), \( \text{N} = 14.01 \), \( \text{O} = 16.00 \) for simplicity here, but for accuracy, use the most precise values.)

2. \( \text{Cl}_2 \)

Step 1: Identify atoms and their counts

• \( \text{Cl} \): 2 atoms

Step 2: Multiply atomic mass by count

• \( \text{Cl} \): \( 2 \times 35.45 = 70.90 \) amu

3. \( \text{Ca(OH)}_2 \)

Step 1: Identify atoms and their counts

• \( \text{Ca} \): 1 atom
• \( \text{O} \): 2 atoms (from the two \( \text{OH}^- \) groups)
• \( \text{H} \): 2 atoms (from the two \( \text{OH}^- \) groups)

Step 2: Multiply each atomic mass by its count

• \( \text{Ca} \): \( 1 \times 40.08 = 40.08 \)
• \( \text{O} \): \( 2 \times 16.00 = 32.00 \)
• \( \text{H} \): \( 2 \times 1.01 = 2.02 \)

Step 3: Sum the masses

\( 40.08 + 32.00 + 2.02 = 74.10 \) amu

4. \( \text{HC}_2\text{H}_3\text{O}_2 \) (Acetic Acid, \( \text{CH}_3\text{COOH} \))

Step 1: Identify atoms and their counts

• \( \text{C} \): 2 atoms
• \( \text{H} \): 4 atoms (wait, \( \text{HC}_2\text{H}_3\text{O}_2 \) is \( \text{C}_2\text{H}_4\text{O}_2 \)? Wait, no: \( \text{HC}_2\text{H}_3\text{O}_2 \) is \( \text{H} + \text{C}_2\text{H}_3\text{O}_2 \), so total \( \text{C}: 2 \), \( \text{H}: 4 \), \( \text{O}: 2 \))

Step 2: Multiply each atomic mass by its count

• \( \text{C} \): \( 2 \times 12.01 = 24.02 \)
• \( \text{H} \): \( 4 \times 1.01 = 4.04 \)
• \( \text{O} \): \( 2 \times 16.00 = 32.00 \)

Step 3: Sum the masses

\( 24.02 + 4.04 + 32.00 = 60.06 \) amu (actual molar mass of acetic acid is ~60.05 g/mol, which matches)

5. \( \text{CO}_2 \)

Step 1: Atoms: \( \text{C}: 1 \), \( \text{O}: 2 \)

Step 2: Masses: \( 12.01 + 2 \times 16.00 = 12.01 + 32.00 = 44.01 \) amu

6. \( \text{N}_2\text{O} \)

Step 1: Atoms: \( \text{N}: 2 \), \( \text{O}: 1 \)

Step 2: Masses: \( 2 \times 14.01 + 16.00 = 28.02 + 16.00 = 44.02 \) amu

7. \( \text{NaOCl} \) (Sodium Hypochlorite)

Step 1: Atoms: \( \text{Na}: 1 \), \( \text{O}: 1 \), \( \text{Cl}: 1 \)

Step 2: Masses: \( 22.99 + 16.00 + 35.45 = 74.44 \) amu

8. \( \text{Ca(NO}_3\text{)}_2 \)

Step 1: Atoms: \( \text{Ca}: 1 \), \( \text{N}: 2 \), \( \text{O}: 6 \) (since 2 nitrate groups, each with 1 N and 3 O)

Step 2: Masses: \( 40.08 + 2 \times 14.01 + 6 \times 16.00 = 40.08 + 28.02 + 96.00 = 164.10 \) amu

9. \( \text{CH}_3\text{OH} \) (Methanol)

Step 1: Atoms: \( \text{C}: 1 \), \( \text{H}: 4 \), \( \text{O}: 1 \)

Step 2: Masses: \( 12.01 + 4 \times 1.01 + 16.00 = 12.01 + 4.04 + 16.00 = 32.05 \) amu

10. \( \text{H}_2\text{SO}_4 \) (Sulfuric Acid)

Step 1: Atoms: \( \text{H}: 2 \), \( \text{S}: 1 \), \( \text{O}: 4 \)

Step 2: Masses: \( 2 \times 1.01 + 32.07 + 4 \times 16.00 = 2.02 + 32.07 + 64.00 = 98.09 \) amu

11. \( \text{CaSO}_4 \) (Calcium Sulfate)

Step 1: Atoms: \( \text{Ca}: 1 \), \( \text{S}: 1 \), \( \text{O}: 4 \)

Step 2: Masses: \( 40.08 + 32.07 + 4 \times 16.00 = 40.08 + 32.07 + 64.00 = 136.15 \) amu

12. \( \text{CaCl}_2 \) (Calcium Chloride)

Step 1: Atoms: \( \text{Ca}: 1 \), \( \text{Cl}: 2 \)

Step 2: Masses: \( 40.08 + 2 \times 35.45 = 40.08 + 70.90 = 110.98 \) amu

Summary of Molecular Masses (using rounded atomic masses for simplicity; for more precision, use the exact atomic weights from the periodic table):

Compound	Molecular Mass (amu)
\( \text{Cl}_2 \)	70.90
\( \text{Ca(OH)}_2 \)	74.10
\( \text{HC}_2\text{H}_3\text{O}_2 \)	60.06
\( \text{CO}_2 \)	44.01
\( \text{N}_2\text{O} \)	44.02
\( \text{NaOCl} \)	74.44
\( \text{Ca(NO}_3\text{)}_2 \)	164.10
\( \text{CH}_3\text{OH} \)	32.05
\( \text{H}_2\text{SO}_4 \)	98.09
\( \text{CaSO}_4 \)	136.15
\( \text{CaCl}_2 \)	110.98

To calculate each one precisely, follow the same steps: identify the number of each atom, multiply by its atomic mass, and sum. Use the most accurate atomic masses (e.g., from the IUPAC standard) for precise results (e.g., \( \text{Na} = 22.98976928 \), \( \text{N} = 14.0067 \), \( \text{O} = 15.9994 \), \( \text{Cl} = 35.453 \), \( \text{Ca} = 40.078 \), \( \text{H} = 1.00784 \), \( \text{C} = 12.0000 \), \( \text{S} = 32.06 \), etc.).