Question

A sample of gas has a pressure of \[1.2atm\] and a volume of \[2.3L\] . What is the new pressure if the volume is compressed to \[1.1L\] ?

Answer 1

Hint: Ideal gas laws that establish a direct relationship between physical variables like pressure, volume and temperature are followed by ideal gases only. Since the given values only contain information about pressure and temperature, we assume that the gases are ideal in nature.

Complete answer:
The relationship between pressure and volume is an inverse relationship in which the pressure of a fixed amount of gas at a particular temperature is always inversely proportional to the volume of the gas. An increasing pressure results in a decrease in volume and vice-versa. This relation was determined by the Boyle’s law that can be mathematically expressed as follows:
\[{P_1} \times {V_1} = {P_2} \times {V_2}\]
Compression of a gas is a phenomenon by which a gas reduces in its volume. A change in volume is always associated with a corresponding change in pressure, which can be determined by Boyle's law of ideal gases. Assuming that the gas is ideal, we insert the given values of pressure and volume in the above equation. \[{P_2}\] is the unknown final pressure of the gas after being compressed.
\[{P_2} = \dfrac{{{P_1} \times {V_1}}}{{{V_2}}} = \dfrac{{1.2atm \times 2.3L}}{{1.1L}} = 2.50atm\]
\[ \Rightarrow \] Thus, the pressure of the compressed gas is \[2.50atm\].

Note:
The units of pressure will be the same as the given pressure as the units of initial and final volume are the same and cancel each other out. The pressure comes out to be greater than initial pressure as the volume decreases after getting compressed.