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# A person add $1.71$ grams of sugar ${{\text{C}}_{{\text{12}}}}{{\text{H}}_{{\text{22}}}}{{\text{O}}_{{\text{11}}}}$ in order to sweeten his tea. The number of carbon atoms added is (mol. Mass of sugar = $342$):A) $3.6 \times {10^{22}}$ B) $7.2 \times {10^{21}}$ C) $0.05$ D) $6\,.6 \times {10^{22}}$

Last updated date: 02nd Aug 2024
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Hint: We will use the Avogadro number to determine the number of atoms in the given gram. For this first, we have to calculate the moles of He in the given gram. For this, we will use the mole formula. Then by using the Avogadro number we will determine the numbers of atoms.

Formula used: ${\text{mole}}\,\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,\,{\text{mass}}}}$

We will use the mole formula to determine the number of moles of sugar as follows:
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,{\text{mass}}}}$
On substituting $1.71$ grams for mass of sugar and $342$for molar mass of sugar,
${\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{1}}{\text{.71}}}}{{{\text{342}}}}$
${\text{mole}}\,{\text{ = }}\,0.005$
So, the moles of the sugar added in the tea by the person is$\,0.005$.
One mole of any substance =$\,6.02 \times {10^{23}}$ atoms
From the formula of sugar it is clear that one mole of sugar has $12$ carbon atoms.
One mole sugar =$12$ atoms
So, one mole of sugar have,
One mole =$\,6.02 \times {10^{23}}\, \times \,12$ atoms of carbon
So, $\,0.005$moles of sugar will have,
$0.005$mole =$\,6.02 \times {10^{23}}\, \times \,12\, \times \,0.05$ atoms of carbon
$0.005$mole =$3.6 \times {10^{22}}$atoms of carbon
So, the number of carbon atoms added is $3.6 \times {10^{22}}$.

Therefore, option (A) $3.6 \times {10^{22}}$, is the correct answer.

Note: The number of atoms present in $12\,{\text{g}}$ of carbon-12 is known as one mole. The total number of atoms is the sum of all the atoms of a compound. In case of monoatomic, one mole of substance contains Avogadro's number of atoms. In case of an ionic compound, we determine the total number of ions by multiplying the total number of ions with the Avogadro number. The subscript after each atom represents the numbers of that atom. The superscript represents the charge of an ion not the number of that ion.