Understanding the Concept: Moles and Mass
In chemistry, the mole is a fundamental unit used to bridge the gap between the microscopic world of atoms and the macroscopic world we can measure in a laboratory.
Key constants to remember:
- Avogadro’s Constant ($N_A$): $6.022 \times 10^{23}$ particles (atoms or molecules) per mole.
- Atomic Mass: The mass of one mole of an element (in grams), found on the periodic table.
The relationship is defined as: $\text{Mass} = \frac{\text{Number of particles}}{\text{Avogadro's constant}} \times \text{Molar mass}$
Solving the Problems
i) Two atoms of Carbon
To find the mass of a single atom (or a few atoms), we divide the atomic mass of the element by Avogadro’s number.
- Atomic mass of Carbon (C): $12.01 \text{ g/mol}$ (we can use $12 \text{ g/mol}$ for simplicity).
- Number of atoms: $2$.
- Calculation: $\text{Mass} = \frac{2 \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} \times 12 \text{ g/mol}$ $\text{Mass} \approx 3.32 \times 10^{-23} \times 12 \approx 3.986 \times 10^{-23} \text{ grams}$
ii) Three molecules of Hydrogen
Hydrogen gas exists as diatomic molecules ($H_2$).
- **Molar mass of } H_2: Since one H atom is $\approx 1 \text{ g/mol}$, $H_2 = 2 \times 1 \text{ g/mol} = 2 \text{ g/mol}$.
- Number of molecules: $3$.
- Calculation: $\text{Mass} = \frac{3 \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}} \times 2 \text{ g/mol}$ $\text{Mass} \approx 4.98 \times 10^{-24} \times 2 \approx 9.96 \times 10^{-24} \text{ grams}$
Summary of Intuition
Because atoms and molecules are incredibly small, their mass in grams will always be an extremely tiny number. By using Avogadro's number, we treat the sample as a tiny fraction of a mole, allowing us to convert the count of individual particles into a physical weight.