Question

1.0 g of H₂ has the same number of molecules as in:

• A. 14 g of N₂
• B. 18 g of H₂O
• C. 16 g of CO
• D. 28 g of N₂

Answer 1

The Correct Option is A

The problem is to find out which of the given options has the same number of molecules as 1.0 g of H₂. To solve this, we need to understand the concept of moles, which allows us to compare the number of molecules present in different substances.

First, let's calculate the number of moles present in 1.0 g of H₂:
The molar mass of H₂ (hydrogen gas) is 2.0 g/mol.

\[ \text{Number of moles of }\text{H}_2 = \frac{\text{mass of } \text{H}_2}{\text{molar mass of } \text{H}_2} = \frac{1.0 \ \text{g}}{2.0 \ \text{g/mol}} = 0.5 \ \text{mol} \]

The number of molecules present in a mole is given by Avogadro's number, which is approximately 6.022 x 10²³ molecules/mol. So, 0.5 mol of H₂ contains:

\[ 0.5 \ \text{mol} \times 6.022 \times 10^{23} \ \text{molecules/mol} = 3.011 \times 10^{23} \ \text{molecules} \]

Next, let's check which option has the same number of moles (and thus, the same number of molecules) as 0.5 mol:

1. 14 g of N₂
2. 18 g of H₂O
3. 16 g of CO
4. 28 g of N₂

We will calculate the number of moles for each of these substances:

• The molar mass of N₂ is 28 g/mol. So: \[ \text{Number of moles of } \text{N}_2 = \frac{14 \ \text{g}}{28 \ \text{g/mol}} = 0.5 \ \text{mol} \]
• The molar mass of H₂O is 18 g/mol. So: \[ \text{Number of moles of } \text{H}_2\text{O} = \frac{18 \ \text{g}}{18 \ \text{g/mol}} = 1 \ \text{mol} \]
• The molar mass of CO is 28 g/mol. So: \[ \text{Number of moles of } \text{CO} = \frac{16 \ \text{g}}{28 \ \text{g/mol}} \approx 0.57 \ \text{mol} \]
• The molar mass of N₂ is 28 g/mol. So: \[ \text{Number of moles of } \text{N}_2 = \frac{28 \ \text{g}}{28 \ \text{g/mol}} = 1 \ \text{mol} \]

From these calculations, 14 g of N₂ results in 0.5 mol, which is the same number of moles as 1.0 g of H₂. Hence, 14 g of N₂ has the same number of molecules as 1.0 g of H₂.

Conclusion: The correct answer is 14 g of N₂.