Formulas of Gaseous State





Boyle’s law,

P \propto \dfrac{1}{V} PV = Constant

P_1V_1 = P_2V_2  (At constant temperature)

 

Charle’s law;

V \propto T,\\[3mm] \dfrac{V}{T} = \text{Constant} \\ \dfrac{V_1}{T_1} = \dfrac{V_2}{T_2}\text{At constant pressure}

 

Gas equation,

\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}

Ideal gas equation, PV = nRT.

 

Avogadro’s hypothesis;

V \propto N (At const. temperature and pressure)

 

Dalton’s Law,

P = p_1 + p_2 + p_3 \cdots

 

Graham’s law,

\dfrac{r_1}{r_2} = \sqrt{\dfrac{d_2}{d_1}} = \sqrt{\dfrac{M_2}{M_1}}

 

Kinetic gas equation;

PV = \dfrac{1}{3}mnu^2

 

Root mean square velocity;

u = \sqrt{\dfrac{3PV}{M}} = \sqrt{\dfrac{3RT}{M}} = \sqrt{\dfrac{3P}{d}}

 

Average velocity;

v = \sqrt{\dfrac{8RT}{\pi M}} = \sqrt{\dfrac{8PV}{\pi M}} = \sqrt{\dfrac{8P}{ \pi d}}

 

Most probable velocity

\alpha = \sqrt{\dfrac{2RT}{M}} = \sqrt{\dfrac{2PV}{M}} = \sqrt{\dfrac{2P}{d}}

U : v : \alpha = 1.0 : 0.9213 : 0.8177

\alpha : v : u = 1.0 : 1.128 : 1.234

 

Van der Waals equation,

[P + \dfrac{an^2}{V^2}] [V- nb] = nRT

 

Critical components,

V_c = 3b \\[3mm] P_c = \dfrac{a}{27 b^2} \\[3mm] T_c = \dfrac{8a}{27 bR} \\[3mm] \dfrac{P_cV_c}{T_c} = \dfrac{3}{8}R \\[3mm] a = 3V_c^2P_c = \dfrac{27 R^2T_c^2}{64 P_c} \\[3mm] b = \dfrac{V_c}{3} = \dfrac{RT_c}{8P_c} \\[3mm] T_i = \dfrac{2a}{bR} \\[3mm] T_B = \dfrac{a}{bR}

Related posts:

  1. Gaseous State Worksheet There are three states of matter, Solid, Liquid and Gas.The...
  2. The Gas Equation If Boyle’s and Charle’s law are combined, then PV =...
  3. Molecular Velocity Molecular Velocities In kinetic theory of gas the velocity of...
  4. Critical Constants Critical Constants The critical temperature, Tc, is characteristic of every...
  5. Boyle’s Law Boyle’s Law (1662) This law states that, “For a given...