Question

mass of a gas occupies 572 cm3 at 130 degree Celsius and 725 mm of Hg pressure. What will be its
volume at 240C and 792 mm Hg pressure?

Answer 1

Given :

• Initial pressure ( P₁ ) = 725 mm of Hg
• Initial temperature ( T₁ ) = 130° C
• Initial Volume ( V₁ ) = 572 cm³

• Final pressure ( P₂ ) = 792 mm of Hg
• Final temperature ( T₂ ) = 240° C

To find :

Final Volume ( V₂ )

Formula used :

Ideal gas equation : PV = nRT

SOLUTION :

As number of mole of gas remains same , and R is gas constant ( it will also remain same )

PV ∝ T

Now we need to change temperature into Kelvin scale.

T₁ = 130°C

T₁ = 130 + 273

T₁ = 403 K

T₂ = 240°C

T₂ = 240 + 273

T₂ = 513 K

$\sf \implies \: \dfrac{P_1 \times V_1}{P_2\times V_2} \: =\: \dfrac{T_1}{T_2} \\\\\sf \implies \: \dfrac{725 \times 572}{792 \times V_2} = \dfrac{403}{513} \\ \\ \sf \implies \: V_2 \: = \: \frac{725 \times 572}{792} \times \dfrac{513}{403} \\ \\ \sf \implies \: V_2 \: = \: \: \dfrac{414700}{792} \times \dfrac{513}{403} \\ \\ \sf \implies \: V_2 \: = \:523.6 \times 1.27 \\ \\ \sf \implies \: V_2 \: = \: \bold{664.97}$

ANSWER :

Final volume = 664.97 cm³