Question

112 cm³ of nitrogen is collected at a pressure of 720 mm of mercury. If the temperature remains constant, find its volume when the pressure is:

20 cm of mercury.

Answer 1

Step-1: Given data

• Temperature is constant.
• The volume of nitrogen = $112{\mathrm{cm}}^3$
• Pressure of nitrogen= $720\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• Volume to be calculated at $20\mathrm{cm}\mathrm{of}\mathrm{mercury}$

Note that mm of mercury can also be written as mm of Hg (as Hg is a symbol of Mercury)

Step-2: Perform unit conversion

• Either convert mm of mercury to cm of mercury or vice versa as units should be the same for the pressure.
• The relationship between cm of mercury and mm of mercury is as follows 1 cm= 10 mm
• Therefore, $20\mathrm{cm}\mathrm{of}\mathrm{mercury}=20\times 10\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• or $20\mathrm{cm}\mathrm{of}\mathrm{Hg}=200\mathrm{mm}\mathrm{of}\mathrm{Hg}$

Step-3: Apply Boyle's law equation to find out the volume at the given pressure of $200\mathrm{mm}\mathrm{of}\mathrm{mercury}$

Boyle's law: According to Boyle's law, at a constant temperature, pressure is inversely proportional to volume for a given mass of the gas.
or PV= constant

Therefore, according to Boyle's law :
${\mathrm{P}}_1{\mathrm{V}}_1={\mathrm{P}}_2{\mathrm{V}}_2$

• Let the volume of nitrogen at a pressure of 720 mm of mercury= ${\mathrm{V}}_1$ = $112{\mathrm{cm}}^3$
• Let the pressure of nitrogen at volume ${\mathrm{V}}_1$= ${\mathrm{P}}_1$ = $720\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• Let the pressure of nitrogen at volume ${\mathrm{V}}_2$= ${\mathrm{P}}_2$ = $200\mathrm{mm}\mathrm{of}\mathrm{mercury}$
• Let the volume of nitrogen at pressure $200\mathrm{mm}\mathrm{of}\mathrm{mercury}$= ${\mathrm{V}}_2$ (to be calculated)

Substituting the values in the above equation

$$\begin{gathered} 720\times 112=200\times {\mathrm{V}}_2 \\ {\mathrm{V}}_2=\frac{720\times 112}{200} \\ {\mathrm{V}}_2=\frac{80640}{200}=403.2{\mathrm{cm}}^3 \end{gathered}$$

${\mathrm{V}}_2=403.2{\mathrm{cm}}^3$

Hence, the volume (V₂) when pressure is 20 cm of mercury is 403.2 cm³.