Understanding the Concept
In chemistry, the mole is a fundamental unit that bridges the microscopic world of atoms and the macroscopic world of laboratory measurements (grams). The key to converting between these two units is the molar mass of the element or compound.
The Conversion Formula
To move between moles and grams, use the following relationship:
- Grams to Moles: $\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}$
- Moles to Grams: $\text{mass (g)} = \text{moles} \times \text{molar mass (g/mol)}$
Solving the Problems
Problem A: Convert 2.62 moles of C to grams of C
Step 1: Identify the molar mass. Looking at the periodic table, the molar mass of Carbon (C) is approximately $12.01 \text{ g/mol}$.
Step 2: Apply the formula. $$\text{Mass} = 2.62 \text{ mol} \times 12.01 \text{ g/mol}$$ $$\text{Mass} = 31.4662 \text{ g}$$
Rounding to significant figures (based on the input 2.62), we get $31.5 \text{ g of C}$.
Problem B: Convert 28.0 grams of $N_2$ to moles of $N_2$
Step 1: Identify the molar mass. Nitrogen gas exists as a diatomic molecule ($N_2$). The atomic mass of N is $14.01 \text{ g/mol}$. Therefore, the molar mass of $N_2 = 2 \times 14.01 = 28.02 \text{ g/mol}$.
Step 2: Apply the formula. $$\text{Moles} = \frac{28.0 \text{ g}}{28.02 \text{ g/mol}}$$ $$\text{Moles} \approx 0.999 \text{ mol}$$
Rounding to appropriate significant figures, we get $1.00 \text{ mole of } N_2$.
Key Takeaways
- Always identify if you have an element or a molecule: Diatomic elements (like $N_2, O_2, H_2$) require you to double the atomic mass of the individual element.
- Check units: Moles cancel out when multiplying by g/mol, leaving you with grams. Conversely, grams cancel out when dividing by g/mol, leaving you with moles.