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Mole Concept and Avogadro's Number

Which one of ...

Question

Which one of the following contains minimum number of atoms? [All volumes are at same conditions of pressure and temperature ]
(1) 1gm of CO2
(2) 1gm of C8H18 (3) 1gm of C2H6. (4) 1gm of B4H10

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Solution

(1) $1 g m$ of $C O_{2} = \frac{1 mol C O_{2}}{44 gm of C O_{2}} \times \frac{6.023 \times 10^{23} atoms}{1 mol of C O_{2}} = 0.13 \times 10^{23}$ atoms
(2) $1 g m$ of $C_{8} H_{1} 8 = \frac{1 mole C_{8} H_{18}}{114 g m of C_{8} H_{18}} \times \frac{6.023 \times 10^{23} a t o m s}{1 mol of C_{8} H_{18}} = 0.05 \times 10^{23}$ atoms
(3) $1 g m$ of $C_{2} H_{6} = \frac{1 mole C_{2} H_{6}}{30 g m of C_{2} H_{6}} \times \frac{6.023 \times 10^{23} a t o m s}{1 mol of C_{2} H_{6}} = 0.2 \times 10^{23}$ atoms
(4) $1 g m$ of $B_{4} H_{10} = \frac{1 mole B_{4} H_{10}}{53.32 g m of B_{4} H_{10}} \times \frac{6.023 \times 10^{23} a t o m s}{1 mol of B_{4} H_{10}} = 0.1 \times 10^{23}$ atoms

From above values, we can conclude that Option B $1 g m$ of $C_{8} H_{18}$ has less number of atoms.

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