Question

The number of hydrogen atoms present in \(5.4\text{ g}\) of urea is: \[ \text{Given: Molar mass of urea }=60\text{ g mol}^{-1} \] \[ N_A=6.022\times10^{23}\text{ particles mol}^{-1} \]

• A. \(2.168\times10^{22}\)
• B. \(2.168\times10^{23}\)
• C. \(1.084\times10^{22}\)
• D. \(1.084\times10^{23}\)

Hint:

First calculate molecules using moles and Avogadro number, then multiply by the number of atoms present in one molecule.

Answer 1

The Correct Option is B

Step 1: Write the formula of urea.
The molecular formula of urea is: \[ \ce{NH2CONH2} \] It can also be written as: \[ \ce{CO(NH2)2} \]

Step 2: Count hydrogen atoms in one molecule of urea.
In urea: \[ \ce{NH2} \] group appears twice. So total hydrogen atoms are: \[ 2+2=4 \] Thus, one molecule of urea contains: \[ 4 \] hydrogen atoms.

Step 3: Calculate moles of urea.
Given mass of urea: \[ 5.4\text{ g} \] Molar mass of urea: \[ 60\text{ g mol}^{-1} \] Moles of urea: \[ \frac{5.4}{60} \] \[ =0.09\text{ mol} \]

Step 4: Calculate number of urea molecules.
Number of molecules: \[ 0.09\times6.022\times10^{23} \] \[ =5.4198\times10^{22} \]

Step 5: Calculate number of hydrogen atoms.
Each urea molecule contains \(4\) hydrogen atoms. So: \[ \text{Number of H atoms}=4\times5.4198\times10^{22} \] \[ =2.16792\times10^{23} \] \[ \approx2.168\times10^{23} \] Therefore, the number of hydrogen atoms is: \[ 2.168\times10^{23}. \]