Question

$6\times {10}^{22}$ molecules are present in $22.4{\text{dm}}^3$ of chlorine gas at STP. Find the volume of ${\mathrm{SO}}_2$ gas at STP which has $3\times {10}^{19}$ molecules.

Answer 1

Step 1: Given information:

• $6\times {10}^{22}$ molecules are present in $22.4{\text{dm}}^3$ of Chlorine gas $\left({\mathrm{Cl}}_2\right)$ at STP.
• Sulfur dioxide $\left({\mathrm{SO}}_2\right)$ gas at STP has $3\times {10}^{19}$molecules.

Step 2: STP

• STP indicates Standard Temperature and Pressure.
• At STP, temperature$=0^{°}\text{C}$
• At STP, pressure$=1\text{atm}$
• The volume of an ideal gas at STP is $22.4\text{L}$ or $22.4{\text{dm}}^3$.

Step 3: Avogadro's law

• It states that equal volumes of all gases under the conditions of same pressure and temperature involve same number of molecules.

Step 4: Calculation of volume of ${\mathrm{SO}}_2$ at STP

$6\times {10}^{22}$ molecules are present in $22.4{\text{dm}}^3$ of Chlorine.

$6\times {10}^{22}$ molecules will be present in $22.4{\text{dm}}^3$ of Sulfur dioxide (According to Avogadro's Law).

Therefore, $3\times {10}^{19}$molecules will be present in $\frac{22.4{\text{dm}}^3}{6\times {10}^{22}\text{molecules}}\times 3\times {10}^{19}{\text{molecules=1.12×10}}^{-2}{\text{dm}}^3$ of Sulfur dioxide.

Hence, the required volume of ${\mathrm{SO}}_2$ gas at STP is ${\mathrm{1.12\times 10}}^{-2}{\text{dm}}^3$.