5.4_P - Chemistry: Molecular Nature Of Matter And Change

Question

How can a unit of length such as millimetre of mercury (mmHg) be used as a unit of pressure, which has the dimensions of force per unit area?

Step-by-Step Solution

Answer

In a mercury barometer, the pressure is measured from the height of the mercury column in the tube. The height of mercury is directly proportional to the atmospheric pressure, that’s why mmHg can be used as a unit of pressure.

Step 1: Pressure

Pressure is a physical property that is defined as force per unit area. 

Its SI unit is Pascal (Pa).

Step 2: Determination of unit mmHg

In a mercury barometer a glass tube is inverted over a mercury containing tub. The balance between atmospheric pressure and gravitational force results in the rise of the mercury in the glass tube. The atmospheric pressure can be calculated from the height of the mercury column. The height of the mercury column is represented by millimeters of mercury. The derivation below shows the relation between atmospheric pressure and height of the mercury column.

$\begin{array}{rcl}\mathrm{P}& =& \frac{\mathrm{F}}{\mathrm{A}}\\ & =& \frac{\mathrm{mg}}{\mathrm{A}}\\ & =& \frac{\mathrm{\rho V}.\mathrm{g}}{\mathrm{A}}\\ & =& \frac{\mathrm{\rho }.\mathrm{Ah}.\mathrm{g}}{\mathrm{A}}\\ & =& \mathrm{\rho gh}\\ & & \end{array}$ 

With,

$\mathrm{\rho }$ = density of mercury

 $\mathrm{g}$ = acceleration due to gravity

 $\mathrm{h}$ = height of the mercury column

 

Thus, mmHg can be used as the unit of pressure.