Question

A vessel contains 1.6 g of dioxygen at STP (273.15 K, 1 atm pressure). The gas is now transferred to another vessel at constant temperature, where pressure becomes half of the original pressure. Calculate

(i) Volume of the new vessel.

(ii) Number of molecules of dioxygen ?

Answer 1

(i) $P_1=1atm.P_2=\frac{1}{2}=0.5atm,T_1=273.15,V_2=?,V_1=?$

32 g dioxygen occupies = 22.4 L volume at STP

$\therefore$ 1.6 g dioxygen will occupy $=\frac{22.4\times 1.6g}{32g}=1.12L$

$V_1=1.12L$

From Boyle's law (as temperature is constant)

$p_1{V}_1=p_2{V}_2$

$V_2=\frac{p_1{V}_1}{p_2}$

$=\frac{1atm\times 1.12L}{0.6atm}=2.24L$

(ii) Number of moles of dioxygen $\frac{\text{Mass of dioxygen}}{\text{Molar mass of dioxygen}}{n}_{O_2}=\frac{1.6}{32}=0.05mol$
1 mol of dioxygen contains $=6.022\times {10}^{23}$ molecules of dioxygen
$\therefore$ 0.05 mol of dioxygen $=6.022\times {10}^{23}\times 0.05$ molecule of $O_2$
$=0.3011\times {10}^{23}$ molecules
$=3.011\times {10}^{22}$ molecules