Question

A gas occupies 1.12 dm³ at a temperature of 127° C and pressure of 800 mm of mercury. Find its volume at S.T.P.

Answer 1

Step-1: Analyse the given values

• Volume occupied by the gas= $1.12{\mathrm{dm}}^3$
• Pressure of the gas= $800\mathrm{mm}\mathrm{of}\mathrm{Hg}$ and
• Temperature of the gas= $127°\mathrm{C}$
• volume occupied by the gas at STP (Standard Temperature and Pressure)= To be calculated
• Value of temperature at STP= $273\mathrm{K}$
• Value of pressure at STP= $760\mathrm{mm}\mathrm{of}\mathrm{Hg}$

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

Convert $127°\mathrm{C}$ into K using the relationship given below

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

• $127+273=400\mathrm{K}$

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}$800

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

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

$$\begin{gathered} {\mathrm{V}}_1=? \\ {\mathrm{P}}_1=760\mathrm{mm}\mathrm{of}\mathrm{Hg} \\ {\mathrm{T}}_1=273\mathrm{K} \end{gathered}$$

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

$$\begin{gathered} {\mathrm{V}}_2=1.12{\mathrm{dm}}^3 \\ {\mathrm{P}}_2=800\mathrm{mm}\mathrm{of}\mathrm{Hg} \\ {\mathrm{T}}_2=400\mathrm{K} \end{gathered}$$

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

Substituting the values above in the equation (i)

$\frac{760\times {\mathrm{V}}_1}{273}=\frac{800\times 1.12}{400}$

${\mathrm{V}}_1=\frac{800\times 1.12\times 273}{760\times 400}$

${\mathrm{V}}_1=\frac{244608}{304000}=0.80463{\mathrm{cm}}^3$

${\mathrm{V}}_1=0.80463{\mathrm{cm}}^3$