Question

At what pressure a quantity of gas will occupy a volume of 60 ml if it occupies a volume of 100 ml at a pressure of 720 mm, assuming the temperature is constant?
A.700 mm
B.800 mm
C.100 mm
D.1200 mm

Answer 1

Hint: Boyle's law, also known as the Boyle–Mariotte law or Mariotte's law (particularly in France), is an experimental gas law that describes how the pressure of a gas tends to rise as the container capacity decreases. Here we use Boyle's law relationship to solve the problem.

Complete answer: The absolute pressure produced by a given mass of an ideal gas is inversely proportional to the volume it fills if the temperature and amount of gas stay fixed within a closed system, according to a modern version of Boyle's law. For a given quantity of confined gas, the product of pressure and volume is a constant, according to the equation, and this holds true as long as the temperature remains constant. The law can be advantageously phrased as for comparing the same material under two distinct sets of circumstances. The pressure of the gas drops in proportion to the increase in volume, as shown by this equation. Similarly, when the volume of the gas diminishes, the pressure rises.
\[{P_1}{V_1} = {P_2}{V_2}\]
Now
From the given question
${P_1} = $720 mm
${V_1} = $100 ml
${V_2} = $60 ml
Now using the formula
\[\Rightarrow {P_1}{V_1} = {P_2}{V_2}\]
\[\Rightarrow \dfrac{{{P_1}{V_1}}}{{{V_2}}} = {P_2}\]
$\Rightarrow \dfrac{{100 \times 720}}{{60}} = {P_2}$
$ \Rightarrow {P_2} = 1200mm$
Therefore, option D is the correct answer.

Note:
Boyle's law is frequently used to explain how the human body's respiratory system operates. This usually entails describing how the lung capacity may be raised or reduced, resulting in a lower or greater air pressure within them (according to Boyle's law). As air goes from high to low pressure, it creates a pressure differential between the air inside the lungs and the ambient air pressure, resulting in either inhalation or exhalation.