Question

A gas occupies 800 cm3 under 760 mm Hg
pressure. Find under what pressure the gas will
occupy 380 cm3, the temperature remaining
constant.
​

Answer 1

Liquids which do not mix with each other and form separate layers are called immiscible liquids.

Answer 2

Answer:

The gas will exert a pressure of 1600 mm Hg.

Explanation:

We have to solve this question using Boyle's Law.

Statement and mathematical expression of Boyle's Law:

Boyle's Law states that:
"Under constant temperature conditions, the volume change of a fixed mass of gas is inversely proportional to the pressure."

Mathematically, it can be represented as:

$V \propto \frac{1}{P} \\\Rightarrow V = \frac{K}{P}$ [K = proportionality constant whose value depends on the mass of the gas and the temperature of the system]

$\Rightarrow PV = K$............(1)

If we compare two or more gases, then (1) can be written as:

P₁V₁ = P₂V₂ = P₃V₃ = ........ = PₙVₙ = K ................(2)

Calculation:

Given that,
The initial volume occupied by the gas = V₁ = 800 cm³
The initial pressure exerted by the gas = P₁ = 760 mm Hg
The final pressure exerted by the gas = P₂ = x (let)
The final volume occupied by the gas = V₂ = 380 cm³

∴ By the problem,

$P_{1}V_{1}= P_{2}V_{2} \\ \Rightarrow 760 \times 800 = x \times 380 \\\Rightarrow x = \frac{760 \times 800}{380} \\\Rightarrow x = 1600$

∴ P₂ = the final pressure exerted by the gas = 1600 mm Hg.

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