Question

A gas occupies a volume of 250 ml at 745 mm Hg and 25∘C. What additional pressure is required to reduce the gas volume to 200 ml at the same time?
A. \[180.25{\text{ }}mm\]
B. \[200.9{\text{ }}mm\]
C. \[186.25{\text{ }}mm\]
D. \[189.4{\text{ }}mm\]

Answer 1

Hint: The force of all gas particle/wall collisions divided by the area of the wall equals pressure (P): Pressure is one of the fundamental quantifiable quantities of this phase of matter, and it is exerted by all gases.

Complete answer:
Boyle’s law - Boyle's law, also known as Mariotte's law, is a relationship that describes how a gas compresses and expands at a constant temperature. At constant temperature, the pressure (p) of a given quantity of gas changes inversely with its volume (v), according to this empirical relationship proposed by physicist Robert Boyle in 1662.
As given in the question ${P_1} = 745mm {\kern 1pt} {\kern 1pt} {\kern 1pt} Hg$
${V_1} = 250ml$
${V_2} = 200ml$
Therefore, by applying Boyle’s law as the temperature is constant.
${P_2} = \dfrac{{{P_1}{V_1}}}{{{V_2}}}$
Substituting the values
${P_2} = \dfrac{{745 \times 250}}{{200}}$
${P_2} = 931.25mm{\kern 1pt} {\kern 1pt} Hg$
Therefore, additional pressure requires is $(931.25 - 745) = 186.25mm$
So, the final answer is option(C) i.e., \[186.25mm\].

Note:
Its volume grows as the pressure is reduced. When you fill your bike tyres with air, you can see a real-life application of Boyle's Law. When you inflate a tyre, the gas molecules inside it are squeezed and packed closer together. Our own breathing is a significant instance of Boyle's law.