Question

${P_1}{V_1} = {P_2}{V_2}$ is correct for which law?
A) Boyle’s law
B) Charles law
C) Ideal gas equation
D) Combined gas law
E) Dalton’s law of partial pressure

Answer 1

Hint: You can recall the gas laws which comprise of the five primary laws namely (i) Charles' Law, (ii) Boyle's Law, (iii) Avogadro's Law, (iv) Gay-Lussac Law and (v) Combined Gas Law. These five gas laws invented the relationship between temperature, pressure, volume and the amount of gas.

Complete step by step solution:
Now, let us look at each law given in the options one by one:
Option A: Boyle’s law: Boyle's Law states that the volume of gas is inversely proportional to the pressure. In other words, it states that for an ideal gas under constant temperature the product of pressure and volume is always a constant provided there is no change in the number of moles of gas. It can be expressed as $ {P_1}{V_1} = {P_2}{V_2} $ where P1 is first pressure, V1 is first volume, P2 is second pressure, and V2 is second volume.
Option B: Charles law: Charles' Law states that the volume of gas is directly proportional to the temperature provided the pressure is kept constant. It can be expressed as $ \dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}} $ where V1 is first volume, V2 is second volume, T1 is first temperature and T2 is second temperature.
Option C: Ideal gas equation: The ideal gas equation refers to the equation of a state of hypothetical ideal gas and is expressed as $ PV = nRT $ where P is pressure, V is volume, n is amount of substance, R is ideal gas constant and T is temperature.
Option D: Combined gas law: Combined gas law states that volume of a given amount of gas is proportional to its temperature and pressure. It can be expressed as $ \dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}} $ where P1 is first pressure, V1 is first volume, P2 is second pressure, V2 is second volume, T1 is first temperature and T2 is second temperature.
Option E: Dalton’s law of partial pressure: Dalton's law states that the total pressure is the sum of individual partial pressures at a constant temperature. This law is basically correlated to the ideal gas law. It can be represented mathematically as follows:
$ {P_{total}} = {P_1} + {P_2} + {P_3} + ........ + {P_n}$
$ {P_{total}} = \sum\limits_{i = 1}^n {{P_i}} $
Hence, from the above discussion, it is clear now that $ {P_1}{V_1} = {P_2}{V_2} $ is correct for Boyle’s law. Thus Option A is correct.

Note:
In numerical problems where the nature of gas is provided as a Real gas, Boyle’s law becomes invalid. Real gases refer to the non-ideal which do not follow the ideal gas law exactly. For real gases, two changes have been incorporated like (i) a constant has been added to the pressure (P) and (ii) a different constant has been subtracted from the volume (V). Thus, the new equation for real gas law is: $ (P + a{n^2}) \times (V - nb) = nRT $.