Question

What is number of hydrogen molecules needed to synthesize 3.4 g of ammonia by reaction with nitrogen?

• A. \(6.022\times 10^{23}\)
• B. \(1.2044\times 10^{23}\)
• C. \(1.8066\times 10^{23}\)
• D. \(1.8044\times 10^{24}\)

Hint:

Write N2 + 3H2 -> 2NH3, find moles of NH3 and use the 3:2 ratio.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The balanced reaction fixes the mole ratio of hydrogen to ammonia. One mole of any gas has \(6.022 \times 10^{23}\) molecules (Avogadro number).

Step 2: Key Formula or Approach
\[ \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \]
So 3 mol \(\text{H}_2\) gives 2 mol \(\text{NH}_3\).

Step 3: Detailed Explanation
Molar mass of \(\text{NH}_3\) = 14 + 3 = 17 g/mol.
Moles of ammonia:
\[ n_{\text{NH}_3} = \frac{3.4}{17} = 0.2 \text{ mol} \]
Moles of hydrogen needed:
\[ n_{\text{H}_2} = 0.2 \times \frac{3}{2} = 0.3 \text{ mol} \]
Number of molecules:
\[ 0.3 \times 6.022 \times 10^{23} = 1.8066 \times 10^{23} \]
Option (B) is the number for 0.2 mol, which wrongly uses a 1:1 ratio. Option (A) is for 1 mol.

Final Answer:
About \(1.8066 \times 10^{23}\) hydrogen molecules are needed, option (C). \[ \boxed{1.8066 \times 10^{23}} \]