Q.What will be the mass of one $^{12}C$ atom in g?

Concept: Molecular Mass Calculation using Avogadro's number

The atomic mass of $^{12}C$ is defined as exactly $12 \, \text{u}$ (unified atomic mass units), where $1 \, \text{u} = 1.66054 \times 10^{-24} \, \text{g}$.

Alternatively, we know that $12 \, \text{g}$ of $^{12}C$ contains exactly $N_A = 6.022 \times 10^{23}$ atoms (Avogadro's number, by definition of the mole).

Therefore, the mass of one $^{12}C$ atom is: …

The carbon-12 isotope is the reference standard for atomic mass. By definition, one mole of $^{12}C$ atoms has a mass of exactly 12 grams, and one mole contains $N_A = 6.022 \times 10^{23}$ atoms (Avogadro's number). This connection between the macroscopic world (grams, moles) and the atomic world (individual atoms) is what lets us calculate the mass of a single atom.

The logic is straightforward: if $6.022 \times 10^{23}$ atoms together weigh 12 g, then one atom weighs that total divided by the number of atoms.

Calculation

1. Identify the molar mass of $^{12}C$ By the definition of the atomic mass unit scale, the molar mass of $^{12}C$ is exactly:

2. Recall Avogadro's number One mole contains:

3. Divide molar mass by the number of atoms per mole The mass of one atom is:

4. Perform the division …

Concept: Molecular Mass Calculation

The mass of one atom is found using the molar mass and Avogadro’s number.

• Step 1: Molar mass of $^{12}\text{C}$ is exactly 12 g/mol.
• Step 2: One mole contains $6.022 \times 10^{23}$ atoms (Avogadro’s number). …

Common Mistakes in Molecular Mass Calculation (Glucose)

Here are the most frequent errors students make when calculating the molecular mass of glucose ($C_6H_{12}O_6$), along with how to avoid each.

1. Using Wrong Atomic Mass Values

The Mistake:

Students often use approximate values like $C = 12$, $H = 1$, $O = 16$ without checking the problem's requirement. Some exam questions expect precise values (e.g., $C = 12.01$, $H = 1.008$, $O = 16.00$).

How to Avoid:

• Always read the question carefully — if it says "atomic masses" or gives a table, use those exact values.
• For standard CBSE/ICSE exams, the accepted values are:
  • $C = 12.0 \, \text{u}$
  • $H = 1.0 \, \text{u}$
  • $O = 16.0 \, \text{u}$
• If no values are given, use the standard ones above.

2. Miscounting the Number of Atoms

The Mistake:

Misreading the subscript — for example, thinking glucose has 6 oxygen atoms (correct) but accidentally using 12 for hydrogen (correct) or 6 for carbon (correct). The error often comes from rushing.

How to Avoid:

• Write the formula clearly: $C_6H_{12}O_6$
• Count each element separately:
  • Carbon: 6 atoms
  • Hydrogen: 12 atoms
  • Oxygen: 6 atoms
• Double-check by adding subscripts: $6 + 12 + 6 = 24$ atoms total.

3. Forgetting to Multiply Atomic Mass by Number of Atoms

The Mistake:

Adding atomic masses directly without multiplying by the subscript. For example:

$12 + 1 + 16 = 29 \, \text{u}$ (wrong!)

How to Avoid:

• Use the formula: $\text{Molecular mass} = (\text{atomic mass of C} \times 6) + (\text{atomic mass of H} \times 12) + (\text{atomic mass of O} \times 6)$
• Write each term separately:
  • Carbon: $12 \times 6 = 72$
  • Hydrogen: $1 \times 12 = 12$
  • Oxygen: $16 \times 6 = 96$
• Then add: $72 + 12 + 96 = 180 \, \text{u}$

4. Arithmetic Errors in Addition

The Mistake:

Simple addition mistakes, e.g., $72 + 12 = 84$ (correct), then $84 + 96 = 180$ (correct), but sometimes students write $180$ as $190$ or $170$.

How to Avoid:

• Do the addition step-by-step:
  • $72 + 12 = 84$
  • $84 + 96 = 180$
• Verify by adding in a different order: $96 + 72 = 168$, then $168 + 12 = 180$.
• Use a calculator if allowed, but always recheck mentally.

5. Confusing Molecular Mass with Molar Mass

The Mistake:

Writing the answer as $180 \, \text{g}$ instead of $180 \, \text{u}$ (atomic mass units). Molecular mass is dimensionless in u, while molar mass is in g/mol.

How to Avoid:

• Molecular mass = sum of atomic masses in u (e.g., $180 \, \text{u}$) …