Rumus gas ideal untuk keadaan yang sama atau berbeda dapat diturunkan dari persamaan:
$\begin {aligned} P \cdot V &= n \cdot R \cdot T \\R &= \dfrac{P \cdot V}{n \cdot T}\end{aligned}$
Dalam hal ini R adalah suatu konstanta/tetapan, nilainya tidak berubah. Untuk keadaan pertama dimisalkan R1 dan keadaan kedua adalah R2.
Karena R adalah tetapan maka
$\begin {aligned}R_1 &= R_2\\\dfrac{P_1 \cdot V_1}{n_1 \cdot T_1} &= \dfrac{P_2 \cdot V_2}{n_2 \cdot T_2}\end{aligned}$
Berikut ini adalah tabel yang dapat digunakan untuk mempelajari proses penurunan rumus-rumus terkait gas ideal untuk variabel pada keadaan yang sama atau berbeda.
Sila centang untuk variabel yang nilainya sama (keadaan yang sama) atau tetap atau tidak berubah. Maka pada output diberikan rumus yang berlaku pada keadaan tersebut.
| No | Variabel Konstan Selain R | Hubungan Variabel Gas-Gas dalam Pers. $PV = nRT$ atau $R = \dfrac{P.V}{n.T}$ | |
|---|---|---|---|
| 1 | $\dfrac{P_1.V_1}{n_1.T_1} = \dfrac{P_2.V_2}{n_2.T_2}$ | ||
| 2 | $P_1=P_2$ dan $V_1=V_2$ | $\dfrac{\color{blue}{\bcancel{\color{black}{P_1}}}\color{red}{\bcancel{\color{black}{V_1}}}}{n_1.T_1} =\dfrac{\color{blue}{\bcancel{\color{black}{P_2}}}\color{red}{\bcancel{\color{black}{V_2}}}}{n_2.T_2}$ | $n_1.T_1=n_2.T_2$ |
| 3 | $P_1=P_2$ dan $n_1=n_2$ | $\dfrac{\color{blue}{\bcancel{\color{black}{P_1}}}\color{black}.V_1}{\color{red}{\bcancel{\color{black}{n_1}}}\color{black}{T_1}} =\dfrac{\color{blue}{\bcancel{\color{black}{P_2}}}\color{black}.V_2}{\color{red}{\bcancel{\color{black}{n_2}}}\color{black}{T_2}}$ | Hukum Charles $\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}$ |
| 4 | $P_1=P_2$ dan $T_1=T_2$ | $\dfrac{\color{blue}{\bcancel{\color{black}{P_1}}}\color{black}.V_1}{n_1.\color{red}{\bcancel{\color{black}{T_1}}}} =\dfrac{\color{blue}{\bcancel{\color{black}{P_2}}}\color{black}.V_2}{n_2.\color{red}{\bcancel{\color{black}{T_2}}}}$ | Hukum Avogadro $\dfrac{V_1}{n_1} = \dfrac{V_2}{n_2}$ |
| 5 | $V_1=V_2$ dan $n_1=n_2$ | $\dfrac{P_1\color{blue}{\bcancel{\color{black}{V_1}}}}{\color{red}{\bcancel{\color{black}{n_1}}}\color{black}{T_1}} =\dfrac{P_2\color{blue}{\bcancel{\color{black}{V_2}}}}{\color{red}{\bcancel{\color{black}{n_2}}}\color{black}{T_2}}$ | Hukum Gay-Lussac $\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}$ |
| 6 | $V_1=V_2$ dan $T_1=T_2$ | $\dfrac{P_1\color{blue}{\bcancel{\color{black}{V_1}}}}{n_1.\color{red}{\bcancel{\color{black}{T_1}}}} =\dfrac{P_2\color{blue}{\bcancel{\color{black}{V_2}}}}{n_2.\color{red}{\bcancel{\color{black}{T_2}}}}$ | Hukum Diver $\dfrac{P_1}{n_1} = \dfrac{P_2}{n_2}$ |
| 7 | $n_1=n_2$ dan $T_1=T_2$ | $\dfrac{P_1.V_1}{\color{blue}{\bcancel{\color{black}{n_1}}}\color{red}{\bcancel{\color{black}{T_1}}}} = \dfrac{P_2.V_2}{\color{blue}{\bcancel{\color{black}{n_2}}}\color{red}{\bcancel{\color{black}{T_2}}}}$ | Hukum Boyle $P_1.V_1=P_2.V_2$ |
| $P$ = tekanan (atm); $V$ = Volume (L); $n$ = Jumlah zat (mol); $R$ = tetapan gas (0,08206 $\frac{atm.L}{mol.K}$); T = Temperatur (K) | |||
| 8 | $P_1=P_2$ | $\dfrac{\color{blue}{\bcancel{\color{black}{P_1}}}.\color{black}V_1}{n_1.T_1} =\dfrac{\color{blue}{\bcancel{\color{black}{P_2}}}.\color{black}V_2}{n_2.T_2}$ | $\dfrac{V_1}{n_1.T_1} = \dfrac{V_2}{n_2.T_2}$ |
| 9 | $V_1=V_2$ | $\dfrac{P_1\color{blue}{\bcancel{\color{black}{V_1}}}}{n_1.T_1} =\dfrac{P_2\color{blue}{\bcancel{\color{black}{V_2}}}}{n_2.T_2}$ | $\dfrac{P_1}{n_1.T_1} = \dfrac{P_2}{n_2.T_2}$ |
| 10 | $n_1=n_2$ | $\dfrac{P_1.V_1}{\color{red}{\bcancel{\color{black}{n_1}}}\color{black}{T_1}} =\dfrac{P_2.V_2}{\color{red}{\bcancel{\color{black}{n_2}}}\color{black}{T_2}}$ | $\dfrac{P_1.V_1}{T_1} = \dfrac{P_2.V_2}{T_2}$ |
| 11 | $T_1=T_2$ | $\dfrac{P_1.V_1}{n_1.\color{red}{\bcancel{\color{black}{T_1}}}} =\dfrac{P_2.V_2}{n_2.\color{red}{\bcancel{\color{black}{T_2}}}}$ | $\dfrac{P_1.V_1}{n_1} = \dfrac{P_2.V_2}{n_2}$ |
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