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: Moles of product
$3.4 \text{ g} / 17 \text{ g mol}^{-1} = 0.2$ mol of ammonia.

Step 2: Use the equation
From $\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3$, each 2 mol of ammonia needs 3 mol of hydrogen, so 0.2 mol needs 0.3 mol.

Step 3: Count molecules
$0.3 \times 6.022 \times 10^{23} = 1.8066 \times 10^{23}$. This matches option (C); (A) is 1 mol and (B) is 0.2 mol.

Final Answer:
Option (C) is correct. \[ \boxed{1.8066 \times 10^{23}} \]