Important Gaseous State Formulas For JEE Main and Advanced

Here is the list of all Gaseous State formulas. The list is very helpful in helping students revise all the important points quickly before the JEE Main or Advanced Exam.

Gaseous State Formulas

  1. Temperature Scale :

C01000=K273373273=F3221232=RR(0)R(100)R(0)\frac{C-0}{100-0} = \frac{K-273}{373-273}=\frac{ F-32}{212-32}=\frac{R-R(0)}{R(100) – R(0)}

Here, R = Temp. on an unknown scale.

  1. Boyle’s law and measurement of pressure:

At constant temperature,

Vα1PV \alpha \frac{1}{ P }

P1V1=P2V2P _{1} V _{1}= P _{2} V _{2}

  1. Charles law:

At constant pressure,

VTV \propto T

OR

V1T1=V2T2\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}

  1. Gay-lussac’s law:

At constant volume,

PαT\quad P \alpha T

P1T1=P2T2temponabsolutescale\frac{ P _{1}}{ T _{1}}=\frac{ P _{2}}{ T _{2}} \rightarrow temp\: on\: absolute\: scale

  1. Ideal gas Equation:

PV = nRT

PV=wmRTOrP=dmRTOrPm=dRTPV =\frac{ w }{ m } RT\: Or\: P =\frac{ d }{ m } RT\: Or\: Pm = dRT

  1. Dalton’s law of partial pressure:

P1=n1RTv,P2=n2RTv,P3=n3RTvP _{1}=\frac{ n _{1} RT }{ v }, \quad P _{2}=\frac{ n _{2} RT }{ v }, \quad P _{3}=\frac{ n _{3} RT }{ v } and so on.

Total pressure = P1+P2+P3+P _{1}+ P _{2}+ P _{3}+\ldots \ldots.

Partial pressure = mole fraction X Total pressure.

  1. Amagat’s law of partial volume:

V=V1+V2+V3+V = V _{1}+ V _{2}+ V _{3}+\ldots \ldots.

  1. Average molecular mass of gaseous mixture:

Mmx= Total mass of mixture  Total no. of moles in mixture =n1M1+n2M2+n3M3n1+n2+n3M _{ mx }=\frac{\text { Total mass of mixture }}{\text { Total no. of moles in mixture }} =\frac{ n _{1} M _{1}+ n _{2} M _{2}+ n _{3} M _{3}}{ n _{1}+ n _{2}+ n _{3}}

  1. Graham’s Law:

Rateofdiffusionr1d;d=densityofgasRate\: of\: diffusion\: r \propto \frac{1}{\sqrt{ d }} ; d = density of gas

r1r2=d2d1=M2M1=VD2VD1\frac{r_{1}}{r_{2}}=\frac{\sqrt{d_{2}}}{\sqrt{d_{1}}}=\frac{\sqrt{M_{2}}}{\sqrt{M_{1}}}=\sqrt{\frac{V \cdot D_{2}}{V \cdot D_{1}}}

  1. Kinetic Theory of Gases:
  • PV=13mNU2PV =\frac{1}{3} mN \overline{ U ^{2}} \quad Kinetic equation of gases
  • Average K.E. for one mole = NA(12mUˉ2)=32KNAT=32RTN_{A}\left(\frac{1}{2} m \bar{U}^{2}\right)=\frac{3}{2} K N_{A} T=\frac{3}{2} R T
  • Root mean square speed
    Urms=3RTMU_{ rms }=\sqrt{\frac{3 RT }{ M }}
    molar mass must be in kg/mole.
  • Average speed
    Uav=U1+U2+U3+UNU _{ av }= U _{1}+ U _{2}+ U _{3}+\ldots \ldots \ldots \ldots U _{ N }
    Uavg. =8RTπM=8KTπmU_{\text {avg. }}=\sqrt{\frac{8 R T}{\pi M}}=\sqrt{\frac{8 K T}{\pi m}}

K is Boltzmman constant

  • Most probable speed
    UMPS=2RTM=2KTmU_{ MPS }=\sqrt{\frac{2 RT }{ M }}=\sqrt{\frac{2 KT }{ m }}
  1. Van Der wall’s equation:

(P+an2v2)(vnb)=nRT\left(P+\frac{a n^{2}}{v^{2}}\right)(v-n b)=n R T

  1. Critical constants:

Vc=3bV_{c}=3 b,

Pc=a27b2P_{c}=\frac{a}{27 b^{2}},

Tc=8a27RbT _{ c }=\frac{8 a }{27 Rb }

  1. Van Der Waal equation in virial form :

z=(1+bVm+b2Vm2+b3Vm3+)aVmRT=1+1Vm(baRT)+b2Vm2+b3Vm3+z=\left(1+\frac{b}{V_{m}}+\frac{b^{2}}{V_{m}^{2}}+\frac{b^{3}}{V_{m}^{3}}+\ldots \ldots \ldots\right)-\frac{a}{V_{m} R T} =1+\frac{1}{V_{m}}\left(b-\frac{a}{R T}\right)+\frac{b^{2}}{V_{m}^{2}}+\frac{b^{3}}{V_{m}^{3}}+\ldots \ldots \ldots \ldots \ldots

  1. Reduced Equation of state:

(Pr+3Vr2)(3Vr1)=8Tr\left(P_{r}+\frac{3}{V_{r}^{2}}\right)\left(3 V_{r}-1\right)=8 T_{r}

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