Question

A gas occupies 560 cm³ at S.T.P. Find its volume when:

The pressure is 800 mm of mercury and the temperature is -173° C.

Answer 1

Step-1: Analyse the given values

• The volume occupied by the gas at STP (Standard Temperature and Pressure)= $560{\mathrm{cm}}^3$
• Value of temperature at STP= $273\mathrm{K}$
• Value of pressure at STP= $760\mathrm{mm}\mathrm{of}\mathrm{Hg}$
• Volume to be calculated at pressure= $800\mathrm{mm}\mathrm{of}\mathrm{Hg}$ and Temperature= $-173°\mathrm{C}$

Step-2: Perform the unit conversion from degree Celsius to Kelvin

$\mathrm{Temperature}\mathrm{in}°\mathrm{C}+273=\mathrm{Temperature}\mathrm{in}\mathrm{K}$

$-173+273=100\mathrm{K}$

Step-3: Use the ideal gas equation

Ideal gas equation: Ideal gas equation correlates all the variables, the pressure and temperature with the volume of the gas.

Mathematically,$\frac{\mathrm{PV}}{\mathrm{T}}=\mathrm{constant}$

$\frac{{\mathrm{P}}_1{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{V}}_2}{{\mathrm{T}}_2}$……….(i)

where P₁, V₁ and T₁ are the pressure, volume and temperature at STP i.e.;

$$\begin{gathered} {\mathrm{V}}_1=560{\mathrm{cm}}^3 \\ {\mathrm{P}}_1=760\mathrm{mm}\mathrm{of}\mathrm{Hg} \\ {\mathrm{T}}_1=273\mathrm{K} \end{gathered}$$

where P₂, V₂ and T₂ are the pressure, volume and temperature at final conditions i.e.;

$$\begin{gathered} {\mathrm{V}}_2=? \\ {\mathrm{P}}_2=800\mathrm{mm}\mathrm{of}\mathrm{Hg} \\ {\mathrm{T}}_2=100\mathrm{K} \end{gathered}$$

Step-4: Substitute the values in the ideal gas equation

Substituting the values above in the equation (i)

$\frac{760\times 560}{273}=\frac{800\times {\mathrm{V}}_2}{100}$

${\mathrm{V}}_2=\frac{760\times 560\times 100}{273\times 800}$

${\mathrm{V}}_2=\frac{42560000}{218400}=194.87{\mathrm{cm}}^3$

${\mathrm{V}}_2=194.87{\mathrm{cm}}^3$