Question

Which of the following would weigh least?

[Atomic mass: $Ag=108,N=14,O=16,C=12$]

• A. $2$ grams atom of nitrogen
• B. $1$ mole of silver
• C. $22.4$ litres of oxygen gas at $1$ atmospheric pressure and $273K$
• D. $6.03\times {10}^{23}$ atoms of carbon

Answer 1

The correct option is D $6.03\times {10}^{23}$ atoms of carbon

(A) $2$ grams atom of nitrogen

$1$ gram atom $=1$ mole of $N_2$

$\therefore 2$ grams atom $=2$ mole of $N_2$

$\therefore$ Mass of $2$ moles (w) $=n\times M_{N_2}$

$=2\times 28g=56g$

(B) $1$ mole of silver

Molar mass of silver (M) $=108g/mol$

(C) $22.4$ lit of $O_2$ at $1$ atm and $273K$

Molar volume at STP $=22.4lit/mol$

Molar of $O_2$ (n) $=\frac{V}{V_m}=\frac{22.4}{22.4}mol$

$=1mol$

Molar masses of $O_2\left(M\right)=32g/mol$

$\therefore$ Mass of $O_2\left(w\right)=n\times M{O}_2$

$=1\times 32g=32g$

(D) $6.03\times {10}^{23}$ atoms of $C$

Number of moles $=\frac{N}{N_A}=\frac{6.03\times {10}^{23}}{6.02\times {10}^{23}}$

$=1.002moles$

$\therefore$ Mass of atoms (w) $=n\times M_c$

$=1.002\times 12g$

$=12.024g$

Hence, Option $D$ is correct.