====== Ideal Gas Law ====== ===== Formula ===== * $P$ = Pressure * $V$ = Volume * $n$ = # Particles * $R$ = Gas law constant (($R$ = 8.31 J mol^-1K^1 = 0.0821 L atm mol^-1K^-1 = 62.4 L torr mol^-1K^-1)) * $T$ = Temperature **__MUST BE A UNIT WITH AN ABSOLUTE ZERO TEMPERATURE (Kelvin [K] for example)__** $PV = nRT$ $PV = k$((k is the law's constant)) is Boyle's law, it is the only inverse relationship of the ideal gas law. $\frac{V}{T} = k$ is Charles's law, it is a direct relationship. $\frac{V}{n} = k$ is Avogadro's law, it is also a direct relation. $\frac{P}{T} = k$ is Gay-Lussac's law, it is once again a direct relationship. ===== Standard Conditions (STP) ===== 1 mole of __any__ gas at STP condition will have a volume equal to **22.4 L**. Standard conditions are represented by the following: * $P$ = 1 atm * $T$ = 273 K ===== Derivative Formulas ===== It isn't necessarily required to know these ones as the ideal gas law covers them. ==== Combined Gas Law ==== $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ This can be simplified to (depending on if certain variables are equal on both sides) - $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ - $P_1V_1 = P_2V_2$ - $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ ==== Avogadro's Law ==== $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ ===== Molar Mass Shortcut ===== "Molar Mass kitty cat" > all good cats put $dRT$ over their $P$ $M = \frac{dRT}{P}$ where $M$ is the molar mass, $d$ is the density, and $R$, $T$, and $P$ represent values from the ideal gas law.