An ideal gas is collected by downward displacement of water. Select the correct expression for $P_{g a s}$ according to the diagram $[d_{H g} = 13.6 g / c m^{3}$ ]:

P_{g a s} = P_{a t m} - [a q . T e n s i o n + \frac{h}{13.6}]

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P_{g a s} = P_{a t m} - h d g

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P_{g a s} = P_{a t m} - a q . T e n s i o n + \frac{h}{13.6}

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None of these.

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Solution

The correct option is A $P_{g a s} = P_{a t m} - [a q . T e n s i o n + \frac{h}{13.6}]$
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, $P_{a t m}$ = $P_{g a s}$ + [ $a q . t e n s i o n$ + $\frac{h}{13.6}$ ]

⇒ $P_{g a s}$ = $P_{a t m}$ - [ $a q . t e n s i o n$ + $\frac{h}{13.6}$ ]

Hence, option A is correct.

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