Question

A gas is collected by downward displacement of water. Select the correct expression for $p _{\text {gas }}$ according to figure $\left(d_{H g}=13.6 g cm ^{-3}\right)$

• A. $p _{ gas }= p _{ atm }-\left(\right.$ Aqueous tension $\left.+\frac{ h }{13.6}\right)$
• B. $p _{ gas }= p _{ atm }- hdg$
• C. $p _{ gas }= p _{ atm }-\left(\right.$ Aqueous tension $\left.\times \frac{ h }{13.6}\right)$
• 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, $P _{\text {atm }}= P _{\text {gas }}+\left[\right.$ aq. tension $\left.+\frac{ h }{13.6}\right]$
$\Rightarrow P _{ gas }= P _{ atm }-\left[\right.$ aq. tension $\left.+\frac{ h }{13.6}\right]$