Question

If 0.01 mol of $\mathrm{P_4O_{10}}$ is removed from 0.1 mol, then the remaining molecules of $\mathrm{P_4O_{10}}$ will be:

• A. $ 2.7 \times 10^{22} $
• B. $ 5.4 \times 10^{23} $
• C. $ 5.4 \times 10^{22} $
• D. $ 1.35 \times 10^{23} $

Hint:

Key points to remember:

• Always subtract moles first before conversion
• Avogadro's number relates moles to molecules
• For significant figures, 0.09 has 1 significant figure
• $\mathrm{P_4O_{10}}$ is a discrete molecular unit

Answer 1

The Correct Option is C

Step 1: Calculate remaining moles
Initial moles = 0.1 mol
Removed moles = 0.01 mol
Remaining moles = $0.1 - 0.01 = 0.09$ mol
Step 2: Convert moles to molecules
Using Avogadro's number ($6.022 \times 10^{23}$ molecules/mol): \[ \text{Number of molecules} = 0.09 \times 6.022 \times 10^{23} \] \[ = 5.4198 \times 10^{22} \approx 5.4 \times 10^{22} \]
Step 3: Verify calculation
\[ 0.09 \times 6.022 \times 10^{23} = (9 \times 10^{-2}) \times (6.022 \times 10^{23}) \] \[ = 54.198 \times 10^{21} = 5.4 \times 10^{22} \]
Step 4: Match with options
The calculated value matches option (c).