this presentation contains Boyle's law, Charles's law, Avogadro's law, ideal gas equation, units of gas constant R and significance of PV=nRT

1. 1

2. Gas Pressure in the light of
KMT
• Pressure is defined as the force the gas exerts
on a given area of the container in which it is
contained.
𝑃 =
𝐹
𝐴
2

3. Units of Pressure
• SI unit of pressure is Pascal
P =
𝑁
𝑚2
= 𝑃𝑎
• A Pascal is defined as the force of 1 Newton (N) spread
over an area of 1 m2
• OTHER UNTIS:
• 1 atm = 101325 Pa = 101325 Nm-2
• 1 atm = 101.325 KPa
• 1 atm = 14.7 Psi (Pounds per square inch)
• 1 atm = 760 torr = 760 mm of Hg
• 1 J = 1 Nm = 107ergs = 1 Kgm2s-2
• 1 Cal = 4.18 J
• 1 atm = 1.01325 bar
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4. Effect of change in Pressure on the
Volume of a Gas – Boyle’s Law
Pressure and volume are
inversely related at constant
temperature.
𝑃 ∝
1
𝑉
𝑃 =
𝐾
𝑉
𝑃𝑉 = 𝐾
𝑃1 𝑉1 = 𝐾
𝑃2 𝑉2 = 𝐾
𝑃1 𝑉1 = 𝑃2 𝑉2 4
“Father of Modern Chemistry”
Robert Boyle

5. Boyle’s Law: P1V1 = P2V2

6. Boyle’s Law – Isotherms
• When P of a gas is plotted againstV at different
temperature, hyperbola curves are obtained which are
called Isotherms.
• As the temperature increases, the isotherms goes away
from both the axis.This is due to increase in volume at
higher temperature.
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7. Effect of change in Temperature on
the Volume of gas – Charles’s Law
• At constant Pressure, volume of given
mass of a gas increase or decreases by
decreases by 1/273 times of its original
original volume at 0oC for every 1oC rise
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Jacques-Alexandre Charles

8. Charles’ Law: V1/T1 = V2/T2

9. Derivation of Critical Form of
Charles’s Law
• Suppose the volume of a gas at 0oC =Vo
• Volume at 1oC = 𝑉𝑜 = 𝑉𝑜 + 𝑉𝑜
1
273
• Volume at 2oC = 𝑉𝑜 = 𝑉𝑜 + 𝑉𝑜
2
273
• Volume at toC = 𝑉𝑡 = 𝑉𝑜 + 𝑉𝑜
𝑡
273
𝑉𝑡 = 𝑉𝑜 1 +
𝑡
273
𝑉𝑡 = 𝑉𝑜
273+𝑡
273
𝑡 + 273 = 𝑇 𝐾𝑒𝑙𝑣𝑖𝑛 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
𝑉𝑡 = 𝑉𝑜
𝑇
273
𝑉𝑡 =
𝑉𝑜
273
𝑇 9

10. Charles’s law - Isobar
When volume of gas is
plotted against
temperature at different
pressures, a straight line is
obtained.
Each constant pressure line
is called Isobar.
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11. Absolute Zero
• According to Charles’s law: At constant Pressure,
volume of given mass of a gas increase or decreases
decreases by 1/273 times of its original volume at 0oC
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12. Absolute Zero
• According to Charles’s law: At constant Pressure,
volume of given mass of a gas increase or decreases
decreases by 1/273 times of its original volume at 0oC
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13. Absolute Zero
• At exact -273 oC the volume of a
given mass of gas reduces to zero.
• -273oC = 0K
• The temperature at which the
given volume of a gas reduces to
Zero is called Absolute Zero i.e. 0K
or -273oC.
• Actually all the gases liquefy or
solidify before they reach -273oC.
• This temperature is considered to
as the lowest possible
temperature
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14. Avogadro’s Law
• At constant temperature
and pressure, the volume
of a gas is directly related
to the number of moles.
𝑉 ∝ 𝑛
𝑉 = 𝐾𝑛
𝑉1
𝑛1
=
𝑉2
𝑛2
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Amedeo Avogadro

15. 15
Avogadro’s Law: V1/n1=V2/n2

16. Avogadro’s Law – Molar Volume
• It has been calculated that if we have 1 dm3 of H2
gas, its mass at STP will be 0.09 g
• ∴ 0.09 g H2 at STP = 1 dm3
• 2.016 g of H2 at STP =
1
0.09
× 2.106 = 22.414 𝑑𝑚3
• 2.016 g H2 = 1 mol
• Hence 1 mol H2 at STP will occupy volume 22.414
dm3
• This volume is called Molar volume.
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17. Avogadro’s Law
• Equal volumes of all gases at same
temperature and pressure must contains
equal number of molecules
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18. Ideal Gas Equation
• An equation that shows the effect of simultaneous
changes in pressure and temperature on the
volume of a given gas is called Ideal Gas equation.
• Ideal gas equation is the combination of three gas
laws:
• Boyle’s Law
• Charles’s Law
• Avogadro’s Law
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19. Derivation of Ideal Gas Equation
• According to Boyle’s law: 𝑉 ∝
1
𝑃
… . . (𝑖)
• According to Charles’s law: 𝑉 ∝ 𝑇 … . . (𝑖𝑖)
• According to Avogadro’s law: 𝑉 ∝ 𝑛 … . . (𝑖𝑖𝑖)
• Combining equations (i) (ii) and (iii) we get:
𝑉 ∝
𝑛𝑇
𝑃
𝑉 =
𝑛𝑅𝑇
𝑃
𝑃𝑉 = 𝑛𝑅𝑇
Where R is called General Gas constant.
• If n=1, then PV = RT or
𝑃𝑉
𝑇
= 𝑅
• So,
𝑃1 𝑉1
𝑇1
= 𝑅
• And
𝑃2 𝑉2
𝑇2
= 𝑅
• ∴
𝑃1 𝑉1
𝑇1
=
𝑃2 𝑉2
𝑇2
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20. Significance of Ideal Gas Equation
• Calculation of Molecular mass of gas:
𝑃𝑉 = 𝑛𝑅𝑇
𝑛 =
𝑊
𝑀
Where W = mass of gas and M= Molecular mass
𝑃𝑉 =
𝑊
𝑀
𝑅𝑇
𝑀𝑃𝑉 = 𝑊𝑅𝑇
𝑀 =
𝑊𝑅𝑇
𝑃𝑉
• Calculation of Density of gas:
𝑃𝑉 =
𝑊
𝑀
𝑅𝑇
𝑀𝑃 =
𝑊
𝑉
𝑅𝑇
As
𝑊
𝑉
= 𝑑
𝑀𝑃 = 𝑑𝑅𝑇
𝑑 =
𝑀𝑃
𝑅𝑇
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21. sidra.javedali@gmail.com
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