Understanding the Concept
To find the mass of a single molecule, we need to bridge the gap between the macroscopic world (moles) and the microscopic world (individual atoms/molecules).
Hydrogen gas exists as a diatomic molecule, denoted as $H_2$.
Key Constants
To solve this, we need two fundamental pieces of information:
- Molar Mass of $H_2$: The mass of one mole of hydrogen gas. Since the atomic mass of hydrogen (H) is approximately 1.008 g/mol (often rounded to 1 g/mol), the molar mass of $H_2$ is $2 \times 1.008 \text{ g/mol} \approx 2.016 \text{ g/mol}$.
- Avogadro's Number ($N_A$): The number of particles in one mole, which is approximately $6.022 \times 10^{23} \text{ molecules/mol}$.
Step-by-Step Calculation
Step 1: Identify the formula
The mass of a single molecule can be found by dividing the molar mass of the substance by Avogadro's number:
$$\text{Mass of 1 molecule} = \frac{\text{Molar Mass}}{\text{Avogadro's Number}}$$
Step 2: Plug in the values
Using the standard values:
- Molar Mass of $H_2 = 2.016 \text{ g/mol}$
- Avogadro's Number = $6.022 \times 10^{23} \text{ molecules/mol}$
$$\text{Mass} = \frac{2.016 \text{ g/mol}}{6.022 \times 10^{23} \text{ molecules/mol}}$$
Step 3: Perform the calculation
$$\text{Mass} \approx 0.3348 \times 10^{-23} \text{ g}$$
Expressing this in standard scientific notation: $$\text{Mass} \approx 3.348 \times 10^{-24} \text{ grams}$$
Summary
The mass of a single hydrogen molecule is approximately $3.35 \times 10^{-24}$ grams. This incredibly small number highlights how tiny molecules actually are and why we use the 'mole' concept in chemistry to work with manageable quantities in the laboratory.