Question

What is the number of molecules in 2.125 g of ammonia?

• A. \(6.022\times 10^{23}\)
• B. \(3.011\times 10^{23}\)
• C. \(1.505\times 10^{22}\)
• D. \(7.527\times 10^{22}\)

Hint:

Convert mass to moles using the molar mass, then multiply by Avogadro number.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
The number of molecules in a sample is found by first converting its mass into moles. One mole of any substance holds \(6.022\times10^{23}\) particles (Avogadro number, \(N_A\)).

Step 2: Key Formula or Approach
\[ n=\frac{\text{given mass}}{\text{molar mass}},\qquad \text{Number of molecules}=n\times N_A \]

Step 3: Molar mass of ammonia
Ammonia is \(\text{NH}_3\). Atomic masses are N = 14 and H = 1, so the molar mass is \(14+3\times1=17\ \text{g mol}^{-1}\).

Step 4: Moles present
\[ n=\frac{2.125}{17}=0.125\ \text{mol} \]

Step 5: Number of molecules
\[ N=0.125\times6.022\times10^{23}=7.5275\times10^{22}\approx7.527\times10^{22} \]

Step 6: Check the other options
Option (A) is the value for a full 1 mol (17 g), and (B) is for 0.5 mol (8.5 g). Option (C) is far too small because it would need only about 0.025 mol. Only (D) matches 0.125 mol.

Final Answer:
The sample is 0.125 mol of \(\text{NH}_3\), which holds \(7.527\times10^{22}\) molecules, option (D). \[ \boxed{7.527\times10^{22}} \]