Question

How many molecules of hydrogen are present in 10 g of hydrogen ?

• A. \(6.023 \times 10^{23} \text{ molecules}\)
• B. \(3.01 \times 10^{23} \text{ molecules}\)
• C. \(6.023 \times 10^{24} \text{ molecules}\)
• D. \(3.01 \times 10^{24} \text{ molecules}\)

Answer 1

The Correct Option is D

To determine how many molecules of hydrogen are present in $10 \, \text{g}$ of hydrogen, we need to use the concept of molar mass and Avogadro's number.

1. Understanding the Molar Mass of Hydrogen:
The molecular formula for hydrogen gas is $\text{H}_2$. The atomic mass of hydrogen ($\text{H}$) is approximately $1 \, \text{u}$ (atomic mass unit). Therefore, the molar mass of $\text{H}_2$ is:

$$ \text{Molar mass of } \text{H}_2 = 2 \times 1 \, \text{g/mol} = 2 \, \text{g/mol} $$

2. Calculating the Number of Moles:
The number of moles ($n$) of a substance can be calculated using the formula:

$$ n = \frac{\text{Mass}}{\text{Molar Mass}} $$
Given that the mass of hydrogen is $10 \, \text{g}$ and the molar mass of $\text{H}_2$ is $2 \, \text{g/mol}$, we have:

$$ n = \frac{10 \, \text{g}}{2 \, \text{g/mol}} = 5 \, \text{moles} $$

3. Using Avogadro's Number:
Avogadro's number states that $1 \, \text{mole}$ of any substance contains $6.02 \times 10^{23}$ particles (molecules, atoms, etc.). Therefore, the total number of molecules in $5 \, \text{moles}$ of $\text{H}_2$ is:

$$ \text{Number of molecules} = n \times \text{Avogadro's number} = 5 \times 6.02 \times 10^{23} $$
Simplifying this gives:

$$ \text{Number of molecules} = 3.01 \times 10^{24} \, \text{molecules} $$

4. Conclusion:
The total number of molecules of hydrogen present in $10 \, \text{g}$ of hydrogen is $3.01 \times 10^{24}$.

Final Answer: $ {3.01 \times 10^{24} \, \text{molecules}} $