STATES OF MATTER BOYLE’S LAW At constant temperature, the pressure of a fixed amount of a gas varies inversely with its volume . Methematically , it can be written as p Ȣ 1/V (at constant T and n ) P = k 1 1/V pV = k 1 At constant temperature the product of pressure and volume of a fixed amount of a gas remains constant Let volume of fixed amount of gas at pressure p1 is v1 and at constant temperature on changing pressure p1 to p2 then volume changes v1 to v2 then at constant temperature by Boyle’s law p 1 V 1 = p 2 v 2 = constant P 1 /p 2 = v 2 /v 1 (Pressure – volume relationship)

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Let volume of fixed amount of gas at pressure p1 is v1 and at constant temperature on changing pressure p1 to p2 then volume changes v1 to v2 then at constant temperature by Boyle’s law p 1 V 1 = p 2 v 2 = constant P 1 /p 2 = v 2 /v 1 Curve obtained at constant temperature is called isotherm

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T 3 T2 T1 Pressure (P) Volume (V) T 3 >T 2 >T 1 Graph of pressure of a gas, p vs. 1/V

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CHARLES’ LAW It states that pressure remaining constant, the volume of a fixed mass of a gas is directly proportional to its absolute temperature V T. At constant pressure the volume of fixed amount of gas is decreased or increased by 1/273.15 times of volume at 0° celcius with every decrease or rise of temperature of the gas by 1°celcius. At constant pressure, Volume of fixed amount of gas at 0°C = V˳ Volume of fixed amount of gas at 1°C = V˳+1/273.15×V˳ Volume of fixed amount of gas at t°C = V˳ +t/273.15×V˳ Therefore Vt = V˳+t/273015×V˳ Vt = V˳(1+t/273.15) Each line of the volume vs temperature graph is called isobar. (Temperature – volume relationship) Absolute temperature: It is the temperature at which the volume of the gas becomes 0. but in practice this temperature is not achieved, before reaching this temperature gas becomes liquified . Ȣ

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P 1 <P 2 <P 3< P 4 Volume Temperature ( ° C) -300 -200 -100 0 100 P 1 P 2 P 3 P 4 -273.15 Volume vs temperature (°C) graph .

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GAY LUSSAC’S LAW It states that at constant volume pressure of a fixed amount of a gas varies directly with the Temperature. Mathematically, P Ȣ T p/T = constant = k 3 This relationship can be derived from boyle’s law and charle’s law. Pressure vs temperature ( kelvin ) graph at constant molar volume. Each line of this graph is called isochore .

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V 1 <V 2 <V 3< V 4 Pressure (bar) Temperature (K) 0 100 200 300 400 V 1 V 2 V 3 V 4 Pressure vs temperature (K) graph ( isochores ) of a gas.

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AVOGADRO LAW (volume – amount relationship) It states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. V Ȣ n V 1 /n 1 = V 2 /n 2 The number of molecules in one mole of a gas has been determined to be 6.022×10²³ and is known as avogadro constant.

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Argon 22.37 Carbon dioxide 22.54 Dinitrogen 22.69 Dioxygen 22.69 dihydrogen 22.72 Ideal gas 22.71 Molar volume in litres per mole of some gases at 273.15 K and 1 bar (STP ).

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Ideal gas A gas that follows Boyle’s law, Charles’ law and Avogadro law strickly is called an ideal gas. Such a gas is hypothetical. Ideal gas equation The three laws which we have learnt till now can be combined together in a single equation which is known as ideal gas equation. By Boyle’s law, V Ȣ 1/P -----------①(when T and n are constant) By Charle’s law, V T -----------②(when P and n are constant) By Avogadro law, V n ------------③9when identical condition of P and t are given) On combining all equations, V nT /P V = nRT /P PV = nRT Where R is a proportionality constant. Known a universal gas constant. Ȣ Ȣ Ȣ

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DALTON’S LAW OF PARTIAL PRESSURES It states that at given condition of temperature the total pressure exerted by the mixture of non – reactive gases is equal to the sum of partial pressure of individual gases. Partial pressure : it is he presure exerted by the same amount of individual gas which is taken in mixture under identical condition. If mixture of non-reactive gs containing various gases has total pressure P total and their partial pressures are P 1 + P 2 + P 3 .............

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Let there is a mixture of three non-reactive gasses A,B and C at given temperature (T). Their number of moles be n 1 ,n 2 and n 3 respectively. Their partial pressure be P 1 , P 2 and P 3 respectively. The volume of vessel be V By ideal gas equation PV = nRT P = nRT /V For gas A, partial pressure P 1 = n 1 Rt/V ---------① For gas B, partial pressure P 2 = n 2 RT/V ---------② For gas C, partial pressure P 3 = n 3 RT/V ---------③ Then total pressure of the mixture, by Dalton’s law, P total = P 1 + P 2 + P 3 = n 1 RT/V + n 2 RT/V + n 3 RT/V P total = (n 1 + n 2 + n 3 )RT/V --------------④ Equation ①/eq.④ P 1 /P total =n 1 RT/V × V/(n 1 + n 2 + n 3 )RT P 1 /P total = n 1 /n 1 + n 2 + n 3 P 1 /P total = X 1 [where X 1 = mole fraction of gas A] Therefore P1 = X1 × P total Similarly P 2 = X 2 × P total P 3 = X 3 × P total Therefore Partial pressure = Mole fraction × Total pressure

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Aqueous Tension of Water ( Vapour Pressure) as a function of Temperature Temperature/K Pressure/bar 273.15 0.0060 283.15 0.0121 288.15 0.0168 291.15 0.0204 293.15 0.0230 Temperature/k Pressure/bar 295.15 0.0260 297.15 0.0295 299.15 0.0331 301.15 0.0372 303.15 0.0418

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