Study of Gas Laws — Question 18

(a) P₁ = Initial pressure of the gas = 100 cm Hg

T₁ = Initial temperature of the gas = 273 K

P₂ = Final pressure of the gas = 10 cm Hg

T₂ = Final temperature of the gas = ?

V₁ = V₂ = V [constant volume]

By Gas Law:

$\dfrac{\text{P}_1\times\text{V}_1}{\text{T}_1} = \dfrac{\text{P}_2\times\text{V}_2}{\text{T}_2}$

Substituting the values :

$\dfrac{100 \times \text{V}}{273} = \dfrac{10 \times \text{V}}{\text{T}_2} \\[1em] \text{T}_2 = \dfrac{ 273}{10} \\[1em] \text{T}_2 = 27.3 \text {K} \\[1em]$

∴ When the pressure is 10 cm Hg, the temperature is 27.3 K.

(b) P₁ = Initial pressure of the gas = 100 cm Hg

T₁ = Initial temperature of the gas (ice point) = 273 K

P₂ = Final pressure of the gas = ?

T₂ = Final temperature of the gas = 100°C = 273 + 100 = 373 K

V₁ = V₂ = V [constant volume]

By Gas Law:

$\dfrac{\text{P}_1\times\text{V}_1}{\text{T}_1} = \dfrac{\text{P}_2\times\text{V}_2}{\text{T}_2}$

Substituting the values :

$\dfrac{100 \times \text{V}}{273} = \dfrac{\text{P}_2 \times \text{V}}{373} \\[1em] \text{P}_2 = \dfrac{ 37300}{273} \\[1em] \text{P}_2 = 136.63 \text { cm of Hg} \\[1em]$

∴ When the chamber is brought to 100°C, the pressure is 136.63 cm Hg.