How can I calculate the number of carbon atoms in my signature written with chalk?

Measure the mass of the chalk piece before writing your signature and then after. The difference in mass is the mass of $\text{CaCO}_3$ transferred to the surface.

$$\text{Mass of } \text{CaCO}_3 = \text{Mass of chalk before} - \text{Mass of chalk after}$$

Use the atomic masses of Calcium (Ca), Carbon (C), and Oxygen (O).

$$\text{Molar mass of } \text{CaCO}_3 = \text{Atomic mass of Ca} + \text{Atomic mass of C} + (3 \times \text{Atomic mass of O})$$ $$\text{Molar mass of } \text{CaCO}_3 \approx 40.08\, \text{g/mol} + 12.01\, \text{g/mol} + (3 \times 16.00\, \text{g/mol}) = 100.09\, \text{g/mol}$$

Divide the mass of $\text{CaCO}_3$ used by its molar mass.

$$\text{Moles of } \text{CaCO}_3 = \frac{\text{Mass of } \text{CaCO}_3}{\text{Molar mass of } \text{CaCO}_3}$$

From the chemical formula $\text{CaCO}_3$, there is one carbon atom for every molecule of calcium carbonate. Therefore, the moles of carbon atoms are equal to the moles of $\text{CaCO}_3$.

$$\text{Moles of C atoms} = \text{Moles of } \text{CaCO}_3$$

Multiply the moles of carbon atoms by Avogadro's number ($6.022 \times 10^{23}\, \text{atoms/mol}$).

$$\text{Number of C atoms} = \text{Moles of C atoms} \times (6.022 \times 10^{23}\, \text{atoms/mol})$$

The calculation steps are:

1. Measure the mass of chalk used.
2. Calculate the molar mass of $\text{CaCO}_3$.
3. Calculate moles of $\text{CaCO}_3$.
4. Determine moles of C atoms.
5. Calculate the number of C atoms.