A mercury barometer reads an atmospheric pressure of 760\text{ mmHg}. A small quantity of … — JAMB UTME

A mercury barometer reads an atmospheric pressure of $760\text{ mmHg}$ . A small quantity of volatile liquid is introduced into the space above the mercury column, where it saturates the space with vapour. If the saturated vapour pressure of the liquid at that temperature is $40\text{ mmHg}$ , what is the new height of the mercury column in the barometer tube?

$720\text{ mmHg}$ Answer
B
$800\text{ mmHg}$
C
$760\text{ mmHg}$
D
$40\text{ mmHg}$

Answer

720\text{ mmHg}

Atmospheric pressure supports both the height of the liquid mercury column and the downward pressure exerted by the saturated vapour. Therefore, the height of the mercury column is given by subtracting the saturated vapour pressure (

40\text{ mmHg}

) from atmospheric pressure (

760\text{ mmHg}

), yielding

720\text{ mmHg}

Step-by-Step Solution

Identify the equilibrium condition for atmospheric pressure balancing the barometer contents.

Atmospheric pressure equals the sum of the mercury column pressure and the saturated vapour pressure:

P_{\text{atm}} = P_{\text{Hg}} + P_{\text{SVP}}

The trapped vapour exerts a downward force on top of the liquid mercury column inside the sealed tube.

Substitute the given values into the pressure equation and solve for the mercury height.

760\text{ mmHg} = P_{\text{Hg}} + 40\text{ mmHg} \implies P_{\text{Hg}} = 760\text{ mmHg} - 40\text{ mmHg} = 720\text{ mmHg}

Subtracting the saturated vapour pressure from atmospheric pressure gives the net height of mercury the atmosphere can support.

Key Concept

Effect of Saturated Vapour Pressure on Barometric Height

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