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: Understanding the Topic:
The question belongs to "Some Basic Concepts of Chemistry," specifically the "Mole Concept." Calculating the number of atoms in a given mass of a substance requires several steps: converting mass to moles using molar mass, converting moles to molecules using Avogadro’s number, and finally multiplying by the "atomicity" (number of specific atoms in one molecule). This is a fundamental skill in stoichiometry.
Step 2: Key Formulas and Approach:
The formulas required are:
$n = \text{Mass} / \text{Molar Mass}$
$\text{Number of Molecules} = n \times N_A$
$\text{Number of Atoms} = \text{Molecules} \times \text{Subscript of that atom in the formula}$
Urea formula: $NH_2CONH_2$.

Step 3: Detailed Explanation:

Analyze Urea: The formula for urea is $(NH_2)_2CO$. Counting the atoms, each molecule contains 1 Carbon, 1 Oxygen, 2 Nitrogens, and 4 Hydrogens ($2 \times 2 = 4$).
Calculate Moles of Urea: \[ n = 5.4 \text{ g} / 60 \text{ g/mol} = 0.09 \text{ mol} \]
Calculate Number of Molecules: \[ \text{Molecules} = 0.09 \times 6.022 \times 10^{23} = 0.54198 \times 10^{23} \]
Calculate Hydrogen Atoms: Since each molecule has 4 Hydrogen atoms: \[ \text{H-atoms} = 4 \times 0.54198 \times 10^{23} = 2.16792 \times 10^{23} \]
Rounding to four significant figures gives $2.168 \times 10^{23}$.
Step 4: Final Answer:
The total number of hydrogen atoms is $2.168 \times 10^{23}$, which is option (D).