Question

Which law has the relation; $P_{ 1 }V_{ 1 }\quad =\quad P_{ 2 }V_{ 2 }$?
A.) Boyle’s law
B.) Charle’s law
C.) Ideal gas equation
D.) Combined gas law

Answer 1

Hint: By looking at the given relation we can figure out that here temperature is constant. So, here you just need to find which is applicable to constant temperature only. Now you can easily reach the answer.

Complete step by step answer:

Boyle’s law is for an ideal gas where we say for a given mass of gas, the pressure and the volume of the gas are inversely proportional when the temperature is constant. The energy of an ideal gas is modeled by just the linear motion of the gas atoms.
It can be shown for an ideal gas that the expression PV represents the energy of a given mass of gas as pressure and volume change (but without heat being exchanged with the environment around the gas), hence PV = constant is Boyle’s law for an ideal gas.
So, we can also write this as, $P_{ 1 }V_{ 1 }\quad =\quad P_{ 2 }V_{ 2 }$
where $P_{ 1 }$ and $V_{ 1 }$ are the initial pressure and volume values, and $P_{ 2 }$ and $V_{ 2 }$ are the values of the pressure and volume of the gas after the change.

Therefore, the correct answer to this question is option A.

Note: Let’s get a brief idea about other laws given in the options -
Charle’s law - Charle's law states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure.
Ideal gas equation - The empirical relationships among the volume, the temperature, the pressure, and the amount of a gas can be combined into the ideal gas law,
PV = nRT
Combine gas law - The combined gas law combines the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law. It states that the ratio of the product of pressure and volume and the absolute temperature of a gas is equal to a constant k.
Dalton’s law of partial pressures - Dalton's law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.