Question

A gas is collected by downward displacement of water. Select the correct expression for $p_{\text{gas }}$ according to figure $\left(d_{Hg}=13.6gc{m}^{-3}\right)$

• A. $p_{gas}=p_{atm}-($ Aqueous tension $+\frac{h}{13.6})$
• B. $p_{gas}=p_{atm}-hdg$
• C. $p_{gas}=p_{atm}-($ Aqueous tension $\times \frac{h}{13.6})$
• D. None of these

Answer 1

Answer: (A)

The atmospheric pressure is balanced by the sum of the pressures of gases, the water column of height $h$, and the surface tension of water.
The pressure exerted by a column of water having height $h$ is equal to $\frac{h}{13.6}$ where $13.6$ is the density of mercury.
Thus, $P_{\text{atm }}=P_{\text{gas }}+[$ aq. tension $+\frac{h}{13.6}]$
$\Rightarrow P_{gas}=P_{atm}-[$ aq. tension $+\frac{h}{13.6}]$