Question

a certain volume of a gass is under a pressure of 900 mm of HG when the pressure is increased by 300 mm the gas occupies 2700 ml if this constant temperature calculate the initial volume of a gas

Answer 1

Explanation:

if p1=900

p2=1200

v1=?

v2=2700 ml

so p1v1=p2v2

900*v1=1200*2700

v1=3600ml

Answer 2

GIVEN :-

• A gas of certain volume is under a pressure of 900 mm of Hg

• The volume occupied by the gas when the pressure was increased by 300 mm of Hg is 2700 ml

TO FIND :-

• The volume occupied by the gas initially

SOLUTION :-

$\large {\underline {\boxed {\bigstar {\red {\sf{1atm = 760 \: mm \: of \: Hg}}}}}}$

$\implies \sf \: 900 \: mm \: of \: Hg = \frac{1}{760} \times 900 \: atm \\ \\ \implies {\underline {\boxed {\blue{\sf {\: 900 \: mm \: of \: Hg = 1.18 \: atm}}}}}$

In the same way ,

Final pressure is increased by 300 mm of Hg = 900 mm of Hg + 300 mm of Hg = 1200 mm of Hg

$\implies \sf \: 1200 \: mm \: of \: Hg = \frac{1}{760} \times 1200 \: atm\\ \\ \implies {\underline {\boxed {\blue {\sf {\:1200 \: mm \: of \: Hg = 1.57 \: atm }}}}}$

We have ,

• P₁ = 1.18 atm , P₂ = 1.57 atm
• V₁ = ? , V₂ = 2700 ml = 2.7 litres

According to Boyle's law ,

$\large {\underline {\boxed {\bigstar {\red {\sf{ \: P_1 V_1 = P_2 V_2}}}}}}$

$\implies \sf \: (1.18)( V_1) = (1.57)(2.7) \\ \\ \implies \sf \: V_1 = \frac{1.57 \times 2.7}{1.18} \\ \\ \implies \sf \: V_1 = \frac{4.239}{1.18} \\ \\ \implies {\underline {\bold {\boxed {\blue {\sf{V_1 \approx \: 3.6 \: litres}}}}}}$

∴ The volume occupied by the gas initially is 3.6 litres or 3.59 litres

NOTE :-

Boyle's law is only applicable when the temperature is kept constant