Question

the volume of gas is 2.5l at 800 mmhg. at what pressure will it occupy 4l,at the same temperature

Answer 1

Required Answer:-

Given:

• The volume of a gas is 2.5L at 800 mm of Hg.

To find:

• The pressure at which the volume of gas will be 4L, temperature remaining constant.

Solution:

Here, the concept of Boyle's Law is used. We are provided with Pressure and Volume and we have to find out the pressure of the gas when it's volume is 4L.

Boyle's law states that:- Volume of a given mass of a dry gas is inversely proportional to it's pressure at constant temperature.

Formula:

P₁V₁ = P₂V₂

Here,

• P₁ = 800 mm of Hg.
• V₁ = 2.5L
• P₂ = ? (Unknown)
• V₂ = 4L

By Boyle's Law,

➡ P₁V₁ = P₂V₂

➡ 800 × 2.5 = P₂ × 4

➡ P₂ = 800 × 2.5/4

➡ P₂ = 200 × 2.5 mm of Hg.

➡ P₂ = 25 × 20 mm of Hg.

➡ P₂ = 500mm of Hg.

★ Therefore, at 500mm of Hg pressure, volume of the gas will be 4L, temperature remaining constant.

Answer:

• The pressure of the gas will be - 500mm of Hg.

Answer 2

$\sf \pink{Given}\begin{cases}&\sf{Volume\:of\:the\:gas(V_1)=\bf{2.5\:litres.}} \\ \\ &\sf{Pressure\:of\:the\:gas\:at\:2 5l(P_1)=\bf{800\:mm\:of\:hg}} \\ \\ &\sf{Volume\:of\:the\:gas(V_2)=\bf{4\:litres.}}\end{cases}$

To FinD:-

The pressure of the gas at volume 4l.

Solution:-

Let the pressure be P.

• We have to solve it by Boyle's Law.

☯ According to Boyle's Law,

$\qquad\normalsize{\pink{\underline{\boxed{\bf{P_1V_1=P_2V_2\:\:[T=constant]}}}}}$

$\sf {Here}\begin{cases}&\sf{V_1=\bf{2.5\:litres.}} \\ &\sf{P_1=\bf{800\:mm\:of\:hg}} \\ &\sf{V_2=\bf{4\:litres.}} \\ &\sf{P_2=\bf{P\:mm\:of\:hg}} \\ &\sf{T=temperature}\end{cases}$

• Putting the values,

$\\ :\normalsize\implies{\sf{800\times2.5=P\times4}}$

$\\ :\normalsize\implies{\sf{\dfrac{800\times2.5}{4}=P}}$

$\\ :\normalsize\implies{\sf{\dfrac{\cancel{800}\times2.5}{\cancel{4}}=P}}$

$\\ :\normalsize\implies{\sf{200\times2.5=P}}$

$\\ :\normalsize\implies{\sf{500.0=P}}$

$\\ \quad:\normalsize\implies{\sf{500=P}}$

$\\ \qquad\normalsize\therefore\boxed{\mathfrak{\pink{P_2=500\:mm\:of\:hg.}}}$

The pressure of the gas at volume 4l is 500 mm of hg.

Explore more:-

• What is Boyle's Law?

"Temperature remaining constant - the volume of a given mass of dry gas is - inversely proportional to its pressure.

• V ∝ 1/P [T = constant]