Question

What would be the equation for finding ${P_2}$ given all the other parameters of the combined gas law$?$

Answer 1

First we have to know the three basic laws which give the relationship between the parameters of the combined gas law. then combine all the laws to obtain the ideal gas law or equation. Using ideal gas law obtained the equation for finding ${P_2}$ given all the other parameters of the combined gas law.

Complete answer:
Boyle’s law states that the volume of a gas is inversely proportional to its pressure at constant temperature. i.e., $V\propto \dfrac{1}{P}$.
Charles’s law states that the volume of a gas is directly proportional to its temperature at constant pressure. i.e., $V\propto T$.
Avogadro’s law states that the volume of a gas is directly proportional to the total number of atoms or molecules of a gas at constant temperature and pressure. i.e., $V\propto \;n$, Where $n$ is the number of molecules of a given gas.
Gay-Lussac's law states that at constant volume, the pressure of a gas is directly proportional to the absolute temperature, $P\;\propto \;T$ at constant $V$.
The combined gas law, is derived from Boyle's law, Charles law, and Gay-Lussac’s law.
Combined gas law can be mathematically expressed as
$k = \dfrac{{PV}}{T}$ Where, $P$ is pressure, $T$ is temperature in kelvin, $V$ is volume and $k = nR$ is constant.
When two substances are compared in two different conditions, the law can be stated as,
$\dfrac{{{P_1}{V_1}}}{{{T_1}}} = \dfrac{{{P_2}{V_2}}}{{{T_2}}}$ Where, ${P_1}$ is initial pressure, ${V_1}$ is initial volume, ${T_1}$ is initial temperature ${P_2}$ is final pressure, ${V_2}$ is final volume and ${T_2}$is final temperature.
Hence, the following equation shows how to solve for ${P_2}$.
${P_2} = \dfrac{{{P_1}{V_1}{T_2}}}{{{T_1}{V_2}}}$

Note:
Note that when combining all three gas laws, Charles's law, Avogadro’s law and Boyle’s law, we get $V\propto \;\dfrac{{nT}}{P}$. Then finally, $V = \dfrac{{nRT}}{P}$ where $R$ constant value is known as the universal gas constant. The above equation is known as the ideal gas law.