(Given : Molar mass of urea : $60 \text{ g mol}^{-1}$, $N_A : 6.022 \times 10^{23} \text{ particles mol}^{-1}$)
Hydrogen Atoms Calculation in Urea
This solution details the steps to find the number of hydrogen atoms in a given mass of urea using stoichiometry and Avogadro's number.
Step-by-Step Solution
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Calculate Moles of Urea:
First, determine the number of moles of urea using the given mass and molar mass.
Moles of urea = $ \frac{\text{Mass of urea}}{\text{Molar mass of urea}} $
Moles of urea = $ \frac{5.4 \text{ g}}{60 \text{ g mol}^{-1}} = 0.09 \text{ mol} $
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Calculate Number of Urea Molecules:
Next, find the total number of urea molecules using the moles calculated and Avogadro's number ($N_A$).
Number of urea molecules = Moles of urea $ \times N_A $
Number of urea molecules = $ 0.09 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules mol}^{-1} $
Number of urea molecules = $ 0.54198 \times 10^{23} \text{ molecules} $
- Determine Hydrogen Atoms per Urea Molecule: The chemical formula for urea is $(NH_2)_2CO$, which means each molecule contains 4 hydrogen atoms (2 from each $NH_2$ group).
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Calculate Total Hydrogen Atoms:
Multiply the number of urea molecules by the number of hydrogen atoms per molecule.
Number of H atoms = Number of urea molecules $ \times $ (Number of H atoms per molecule)
Number of H atoms = $ (0.09 \times 6.022 \times 10^{23}) \times 4 $
Number of H atoms = $ 0.36 \times 6.022 \times 10^{23} $
Number of H atoms = $ 2.16792 \times 10^{23} $
Rounding to the required precision, we get $ 2.168 \times 10^{23} $ hydrogen atoms.
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