Q.What will be the mass of one atom of C-12 in grams?

Concept: Molecular Mass Calculation using Avogadro's number

The molar mass of C-12 is defined as exactly $12 \, \text{g/mol}$, meaning one mole of C-12 atoms has a mass of $12 \, \text{g}$.

One mole contains Avogadro's number of atoms: $N_A = 6.022 \times 10^{23} \, \text{atoms/mol}$.

To find the mass of a single C-12 atom, divide the molar mass by Avogadro's number: …

Why this approach works

The carbon-12 isotope is the reference standard for atomic mass. By definition, one mole of C-12 atoms has a mass of exactly 12 grams, and one mole contains Avogadro's number of atoms. This direct relationship lets us find the mass of a single atom through simple division.

The beauty here is that we're working with the very definition that anchors the entire atomic mass scale. Every other atomic mass is measured relative to C-12, so its numbers are exact starting points.

Step-by-step calculation

1. Identify the known quantities

For C-12, we have two exact values by definition:

• Mass of one mole = $12 \text{ g}$ (exactly)
• Number of atoms in one mole = $N_A = 6.022 \times 10^{23}$ (Avogadro's number)

2. Set up the relationship

If $N_A$ atoms together have a mass of 12 g, then one atom has a mass equal to the total mass divided by the number of atoms:

3. Substitute and calculate …

Concept: Atomic Mass Unit and Gram Conversion

The mass of a single atom is incredibly small — so we use the atomic mass unit (amu) as a bridge.

One C-12 atom is the standard: its mass is defined as exactly 12 amu.

Method: Unified Mass–Gram Conversion

Steps

1. Recall the definition

   $1 \, \text{amu} = \frac{1}{12}$ of the mass of one C-12 atom.

2. Know the gram equivalent

   $1 \, \text{amu} = 1.660539 \times 10^{-24} \, \text{g}$

   (This is Avogadro’s number connection: $1 \, \text{g} = 6.022 \times 10^{23} \, \text{amu}$)

3. Mass of one C-12 atom

   Since one C-12 atom has mass $12 \, \text{amu}$: …

Here are the common mistakes students make when calculating the mass of one atom of C-12 in grams, along with how to avoid each.

1. Confusing Atomic Mass Unit (amu) with Grams

The Mistake:

Students often write the answer as 12 g, thinking that since the atomic mass of C-12 is 12 amu, the mass of one atom must be 12 grams.

Why it’s wrong:

12 g is the mass of one mole of C-12 atoms (Avogadro’s number of atoms), not a single atom. One atom is incredibly tiny — about $10^{-23}$ g.

How to Avoid:

Always remember the conversion:

• 1 amu = $1.66 \times 10^{-24}$ g
• Mass of one C-12 atom = 12 amu So, mass in grams = $12 \times 1.66 \times 10^{-24}$ g

2. Forgetting to Divide by Avogadro’s Number

The Mistake:

Some students directly multiply the molar mass (12 g/mol) by Avogadro’s number instead of dividing.

Why it’s wrong:

Molar mass = mass of 1 mole of atoms. To get mass of 1 atom, you must divide by Avogadro’s number ($6.022 \times 10^{23}$).

How to Avoid:

Use the formula:

For C-12:

3. Using the Wrong Value of Avogadro’s Number

The Mistake:

Using $6.022 \times 10^{22}$ or $6.022 \times 10^{24}$ instead of $6.022 \times 10^{23}$.

How to Avoid:

Memorise Avogadro’s number as $6.022 \times 10^{23}$ (particles per mole). Write it down before starting the calculation.

4. Rounding Too Early or Incorrectly

The Mistake:

Rounding intermediate steps (e.g., using 12 ÷ 6 = 2) leads to a final answer like $2 \times 10^{-23}$ g, which is slightly off.

How to Avoid:

Keep full precision until the final step. The correct value is: …