L12 : Nernst Equation Derivation - Electrochemistry, Chemistry, Class 12 Video Lecture

hello friends this video on
electrochemistry part 12 is brought to
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exam its derive this whole Nernst
equation hey see Nernst equation is
based on equilibrium constant this based
on equally briam concept yes this based
on equilibrium concept so let's take a
reaction
Emil's of capital A plus small B moles
of capital B reacts with I mean reacts
and some n electrons are transferred
you did see mole small C moles of
capital C the small D moles of capital T
this is the reaction let suppose I have
right so at any point of time if I want
to find Q q is nothing but what sea
captain Singh into concentration of C
capital D in concentration of D small D
by capital a filtration of a capital B
concentration that is the value of Q at
any point of thing right and at
equilibrium we know that at equilibrium
Q is equal to K so what you get it K is
nothing but the value of Q at
equilibrium right so if Q is less than K
so if Q is less than K the reaction will
move in forward direction if Q is
greater than okay
we actually moving backwards this is
something we know equilibrium concept
right value of Q is nothing but
concentration of reactant by
concentration of sorry concentration of
product by conservation of reactant
adding any given point of time and at
equilibrium the same value of Q becomes
K and so if Q is less than K the
reaction moves forward direction Q is
greater than okay the action moves in
back relation also we know one more
critical equation as Delta G is nothing
but Delta G naught plus RT Ln Q at
any point of time correct this is the
equation I know this is equation let's
suppose 1 this is equation of mark this
V Nolan and Gibbs free energy change is
the Delta G naught plus RT Ln 2 right so
in case in case all these species are 1
molar this ABC we all are one molar
actually all of 1 molar if you see or 1
molar this Q becomes 1 Ln Q become 0 so
Delta G becomes Delta G naught right so
case 1 all species one more that is what
we have seen till now right in Delta G
becomes Delta G naught plus RT ln 1 that
is nothing but Delta G comes to energy
naught that is what we have seen right
now let's talk about the knot this is
Delta G right this is all we know but we
have to find the electric potential
right so what is electric potential we
know that electric potential is nothing
but work done per unit charge to bring a
unit charge from infinite distance to
point of interest
please let me write stagnation electric
potential is work done per unit charge
to bring a unit charge from
infra my distance to the point of
interest the point I am talking about
right from some infinite distance I'm
bringing it to some point Q right so I
can write that work done since it is per
unit charge right so that means nothing
but is nothing but electric potential
electric potential into total charge of
n molecules total charge or n mole of
electrons actually why C because I am
trying to bring some n moles of
electrons right this n moles of
electrons are getting transferred here
so what is the work done in this I have
I have to find total charge on these n
moles of electron into electric
potential correct because there is the
potential you know the electric
potential of that so that is a work done
by the system correct because for this
system let's suppose E is my electric
potential and any is electron n e n n is
the number of electrons that is getting
transferred right so so we have M when
moles actually because will not talk
about that one number I had been talked
about because a mosby mole C Mo's D both
in same volts by default so we to first
find the total charge on n moles of
electron multiplied with the electric
potential will get the work done by the
system correct so first find the charge
on n moles of electric let's do that so
first find the lights charge on envelope
electron see we know that charge of one
electron is what 1.6 0 to 1 9 into 10 to
the power minus 19 Coulomb one electron
right so I have to find cha
of one mole of electron will be what
the same number which we have got to 9
into 10 to power minus 19 coulomb to
multiply with number of electrons in one
mole that is something would have a
greater number there is nothing but 6.0
to 3 into 10 to power 23 because we know
that if you talk about one mole of
electron that means you're talking about
this many electrons correct and that is
nothing but in minus 6/5 you double zero
Coulomb and you call this as 1 f 1
Faraday so charge and 1 mole of
electrons 1 Faraday charge on n mole of
electron is what n Feridun correct so
now we have found the charge on n Mo's
that is nothing but n n we know this way
and what is the electric potential e you
know this also right the world that is
nothing but NF e correct see we're done
is w-work bill is w electric potential
was e we have just assumed E is the
electric potential and the total charge
is electric relation to charge on an
electron is in it
right so work done this work done is
electrical work work done electrical
work done is NFP but in this case in
this chemical reaction right in this
cell we have only electrical work done
there is no mechanical work done correct
because the pressure and temperature is
constant right if net work done is
nothing but electrical work done right
so by Delta G Delta G did me so my Delta
G here will be equal to what work net
and there is re good minus NFE why why -
because the work is done by system
what is done by system see nobody is
doing work on system right system is
doing the reaction is happening on the
system and the system is worth doing the
work so Delta G is minus NFE correct and
with this reaction also we know that if
Delta G is minus NFE Delta G naught will
be what minus NFE not correct instead of
G will put Z naught instead of T will
put a not correct now let's put this
value in this equation this equation so
we will put this Delta G and Delta G
naught in this equation in this equation
so what this equation will become so
Delta G will become minus NFE minus na e
is nothing but Delta G naught is minus
in inor plus RT Ln Q so let's make this
equation little better by dividing whole
sideways minus NF minus NF you see there
is common so we'll divide this by minus
in there myself it's canceled it's
canceled so with this what you get is e
is nothing were he not minus RT by NF Ln
Q so that is my Nernst equation you see
it is derived from this Gibbs energy
equation correct and if you do not want
to use Ln you can use this equation
where e is the Liberty not - 2.303
RT by NF log Y log you because if you
are seeing here instead of Ln I am using
log I know that 2.30 a 1n n is nothing
but 2.303 log can use any of this
equation so this is the derivation of
Nernst equation
so if you see Nernst equation which we
have found have lot of variables
e is equal to e naught minus two point
three zero three RT by NF log Q right
this is what we have found but most of
the experiment the chemists do they do
at 298 Kelvin and they are not a
constant here R is constant if assume
temperature is 298 this becomes constant
and F is constant at 2.30 this is
constant so let's put all the constants
see what you get so we'll be putting TS
298 Kelvin R will put 8.314 Joule per
mole Kelvin and F we know is nothing
worth 9 608 7 Coulomb per or so let's
find the value of this whole thing this
is my variable I'd right let's find the
value of this this becomes 2 point 3 0 3
r is 8.314 please note the agilent's
Joule per mole Kelvin into temperature
right 298 Kelvin by n F n is nothing
sorry n F F it right F is nine six four
eight seven Kelvin per Kelvin can cancel
mole mole cancel so what you get is
0.592 Joule per Coulomb and Joule per
Coulomb is gold this becomes point seven
zero point zero five nine five zero five
nine two what is what the value of this
comes out to be right so I can rewrite
this as e as a naught minus Oh point
zero five nine two world by n log please
hold me here the whole
be involved mentally that is one way of
writing this equation because most of
the equation motion reactions happen at
298 so instead of writing all the
variables here we can simplify this
equation please note this equation is
only for reactions happening at 298
Kelvin that is root SD really thank you
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