Question

The value of Boyle’s Law constant (in S.I. unit) for \[{\text{200 mL}}\] of gas at \[{\text{1}}{\text{.2 atm}}\] pressure is about:
A.\[{\text{240 atm - mL}}\]
B.\[{\text{0}}{\text{.0024 atm - L}}\]
C.\[{\text{24}}{\text{.3 J}}\]
D.\[{\text{0}}{\text{.24 J}}\]

Answer 1

Hint: Boyle’s Law states that the pressure of a fixed mass of a gas bears a constant relationship to the volume of the gas at constant temperature. We shall substitute the values in the given equation.

Formula Used: ${\text{PV}} = {\text{k}}$,
 where P is the pressure of the gas, V is the volume of the gas, while k is Boyle's constant.

Complete Step by step answer:
The pressure of the gas is \[{\text{1}}{\text{.2 atm}}\].
The S.I. unit of pressure is \[{\text{newton/ }}{{\text{m}}^{\text{2}}}\]or Pascal. 1 atm = $101.325$\[{\text{newton/ }}{{\text{m}}^{\text{2}}}\].
Hence, the \[{\text{1}}{\text{.2 atm}}\]= $121.59$ \[{\text{newton/ }}{{\text{m}}^{\text{2}}}\]
The volume of the gas is \[{\text{200 mL}}\], the S.I. the unit of volume is litre.
Hence, \[{\text{200 mL}}\]= $0.2{\text{L}}$
Therefore, Boyle’s Law constant (in S.I. unit), ${\text{k = 121}}{\text{.59}} \times {\text{0}}{\text{.2 = 24}}{\text{.3}}$ Joule.

Hence, the correct answer is option C.

Notes: The Boyle’s Law can also be expressed by the another formula ${{\text{P}}_{\text{1}}}{{\text{V}}_{\text{1}}}{\text{ = }}{{\text{P}}_{\text{2}}}{{\text{V}}_{\text{2}}}$
Where if any three quantities are known then the fourth one can be determined by the formula. This empirical relation was given by Robert Boyle in the year 1642. The same relation was also given by the French physicist Edme Mariotte in 1676. Only ideal gases obey the Boyle’s Law while the real gases obey the Boyle’s Law only at sufficiently low pressures. The product of pressure and volume generally decreases slightly at higher pressures, where the gas begins to depart from its ideal behaviour.
The application of Boyle's Law can be seen as the piston of a cylinder.