Understanding the Basics: Molecules vs. Moles
In chemistry, we often need to switch between the microscopic world (individual atoms and molecules) and the macroscopic world (the amounts we can measure in a lab). To do this, we use two key concepts:
- Molecular Mass: The mass of a single molecule (often expressed in atomic mass units or grams).
- Molar Mass: The mass of one mole ($6.022 \times 10^{23}$ particles) of a substance, expressed in grams per mole (g/mol).
Solving the Problem
Based on the prompt, we are looking to solve two distinct tasks:
- Calculating the mass of one molecule of Nitrogen ($N_2$).
- Calculating the mass of one mole of Carbon Dioxide ($CO_2$).
Part I: Mass of one molecule of Nitrogen ($N_2$)
To find the mass of a single molecule, we use the formula: $$\text{Mass of 1 molecule} = \frac{\text{Molar Mass}}{\text{Avogadro's Number}}$$
- Identify the molar mass of Nitrogen ($N_2$): Nitrogen exists as a diatomic molecule. The atomic mass of one Nitrogen atom is approximately $14.01 \text{ g/mol}$. Therefore, for $N_2$, the molar mass is $2 \times 14.01 = 28.02 \text{ g/mol}$.
- Apply Avogadro's constant ($N_A = 6.022 \times 10^{23} \text{ molecules/mol}$): $$\text{Mass} = \frac{28.02 \text{ g/mol}}{6.022 \times 10^{23} \text{ molecules/mol}}$$ $$\text{Mass} \approx 4.65 \times 10^{-23} \text{ grams}$$
Part II: Mass of one mole of Carbon Dioxide ($CO_2$)
The mass of exactly one mole of any substance is simply its molar mass expressed in grams.
- Find the atomic masses:
- Carbon ($C$) $\approx 12.01 \text{ g/mol}$
- Oxygen ($O$) $\approx 16.00 \text{ g/mol}$
- Calculate the sum for $CO_2$:
- $1 \times \text{C} + 2 \times \text{O}$
- $12.01 + 2(16.00) = 12.01 + 32.00 = 44.01 \text{ g/mol}$
Thus, the mass of one mole of Carbon Dioxide is approximately 44 grams.
Key Takeaways
- Molar mass is the bridge between the count of particles and the measured weight in grams.
- To go from molar mass to a single molecule, divide by Avogadro's number ($6.022 \times 10^{23}$).
- To go from moles to grams, simply multiply the number of moles by the molar mass.