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**Ideal Gas Equation**

Mathematically,

According to

*Boyle’s Law*; at constant T and n,
V 1/P ……….1

According to

*Charles Law*; at constant P and n,
V T ……….2

According to

*Avogadro Law*; at constant T and n,
V n ……….3

From equation 1, 2 and 3;
we get,

V nT/P ……….4

Or, V =R nT/P ……….5

Also, PV = nRT …………..6

Then, R = PV/nT ………..7

Where, R is a gas constant
which is same for all gases and known as

**and equation 6, PV = nRT is known as***Universal Gas Constant**Ideal Gas Equation.*##
**Equation Of State**

Ideal gas equation is
also known as equation of state because it gives relationship between 4
variables i.e. P, V, n and T. which describes state of any gas.

Let if pressure, volume and temperature of fixed
amount of ideal gas changes from P

_{1}, V_{1}, T_{1}to P_{2}, V_{2}, T_{2}then,
P

_{1}V_{1}/T_{1}= nR …………..8
P

_{2}V_{2}/T_{2}= nR …………..9
So, from equation 8 &
9, we get

P

_{1}V_{1}/T_{1}= P_{1}V_{1}/T_{1}………..10
This above equation (eq.
10) is called

**Combined Gas Law**.####
**Density And Molar Mass Of
Gaseous Substances**:

As per Ideal Gas Equation,

PV=nRT

Then, n/V = P/RT

On replacing n by m/M (as
mole n= mass m/ molar mass M); we obtain,

m/MV=P/RT

On replacing m/V by
density d; we obtain,

d/M=P/RT

Also, on rearrangement,

**M = dRT/P**

Where, M is molar mass, d
is density, R is gas constant, T is temperature and P is pressure.

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**Dalton Law Of Partial
Pressure**:

According to Dalton law of
partial pressure, “Total exerted pressure by mixture of all non-reactive gases
is equal to the sum of partial pressure of all individual gases.”

At constant temperature T
and Volume V

P

_{total}= p_{1}+p_{2}+p_{3}…………..
Where, P

_{tolal}= total exerted pressure of mixture of all gases.
p

_{1}, p_{2}, p_{3 }etc. is pressure exerted by individual gases known as partial pressure.####
**Aqueous Tension**:

It is exerted by the
saturated water vapors.

P

_{drygas}= P_{total}– Aqueous Tension####
**Partial Pressure In Terms
Of Mole Fraction**:

Let at T temperature, 3 gases of Volume V exert the partial pressure
p1, p2, p3. Then as per ideal gas equation,

p

_{1}=n_{1}RT/V
p

_{2}=n_{2}RT/V
p

_{3}=n_{3}RT/V
Where,
n

_{1}, n_{2}, n_{3}are no. of moles.
Also, according to Daltons law of partial
pressure

P

_{total}= p_{1}+p_{2}+p_{3}
Or, P

_{total}= n_{1}RT/V + n_{2}RT/V + n_{3}RT/V = (n_{1}+n_{2}+n_{3})RT/V
And,
on dividing p

_{1}by P_{Total }, we obtain
P

_{1}/ P_{Total}={n_{1}/(n_{1}+n_{2}+n_{3})}{RTV/RTV}
P

_{1}/ P_{Total}=n_{1}/(n_{1}+n_{2}+n_{3}) = n_{1}/n = x_{1}
Where,
n= n

_{1}+n_{2}+n_{3}and x_{1}is mole fraction of first gas.
So,
p

_{1}=x_{1}P_{Total}
Similarly,
p

_{2}=x_{2}P_{Total}
P

_{3}=x_{3}P_{Total}
Then,
general equation is written as-

P

_{i}=x_{i}P_{Total}
Where,
p

_{i }is partial pressure of i^{th}gas.
x

_{i }is mole fraction of i^{th}gas.
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