A column of mercury of 10cm length is contained in the middle of a narrow horizontal 1m (100cm) long tube which is closed at both the ends. Both the halves of the tube contain air at a pressure of 76 cm of mercury. By what distance will the column of mercury be displaced if the tube is held vertically?

 

Initially when tube is horizontal then pressure (P) =76 cm Hg and volume (V) =45 cm of tube.

Finally when tube is made vertical, as temperature and pressure are constant, then by gas law

P₁ (45+x)=PV   ……..(1)

(P₁+10)(45-x) =PV……(2)

From equations 1 and 2 find the value of P₁

P₁ =(225-5x)/x

Put the value of P₁ in equation 1 or 2

On calculating the value of x is 2.95 cm

Related questions:

Liquid ammonia bottle is cooled before opening the seal. Explain.

The molecular speeds of gaseous molecules are analogous to those of rifle bullets; why is then odour of the gaseous molecule not detected so fast?

Carbon dioxide is heavier than oxygen and nitrogen but is does not form the lower layer of the atmosphere. Explain.

Out of dry air and wet air, which is heavier?

Can we apply Dalton’s law of partial pressure to a mixture of carbon monoxide and oxygen?

Why a bottle of liquid ammonia is cooled before opening the seal?

Explain , Aerated water bottles are kept under water during summer why?

Arrange the following in the increasing order of melting point of different types of crystalline solid (i) Covalent solid (ii) Metallic solid (iii) Molecular (iv) Ionic

Why falling liquid drops are spherical?

Why diethyl ether has higher vapour pressure than ethyl alcohol at a particular temperature?

Why liquid have a definite volume but no definite shape?

What are the difference between Diffusion and Effusion ?

What is payload of Balloon ?

What is Aqueous tension ?

What is Vander waals equation of state of a real gas ?

What is Boyle's temperature ? and what is relation of Boyle's temperature with Vander waal's constant?

The classroom consists of 30 equidistant rows of benches. A student from first benches release (N2O) nitrous oxide (laughing gas) where a student of last bench releases tear gas (C10H5ClN2=2-chlorobenzalmalononitrile) simultaneously. Find out the which benches students starts laughing and weeping simultaneously.

The Molecular weight (M_A) of N₂O (laughing gas = 44 gm/mol.

Molecular weight (M_B) of (C₁₀H₅ClN₂) (Tear gas) = 179 gm/mol.

(r₁/r₂) = √{ (M_B/M_A) }

(r₁/r₂) =√{ (179/44) }

(r₁/r₂) = √4

(r₁/r₂) = 2

Now let s take “x” as the row from where student start laughing and weeping simultaneously.

Therefore:

(X/30- x) = 2

x = 2(30- x)

 x = 60-2x

3x = 60

  x = 20

Therefore, from 20^th row where students will start weeping and laughing simultaneously.

Related Questions:

Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

A gas occupied a volume of 250 ml at 700 mm Hg pressure and 25°C. What additional pressure is required to reduce the gas volume to its 4/5th value at the same temperature

A sample of a given mass of a gas at a constant temperature occupies 95cm3 under a pressure of 9.962 × 104N/m2 .At the same temperature, it volume at a pressure of 10.13 × 104 N/m2 is :

Calculate the mass of mercuryin a uniform column, 760 mm high and 1.00 cm2 in cross-sectional area. Is there any change in (a) mass and (b) pressure of column of same height but with 2.00 cm2 cross sectional area is taken ? (density of Hg = 13.6 g/cm3 )

1 mole of CCl4 vapours at 77oC occupies a volume of 35.0 L. If vander waal's constants are a = 20.39 L 2 atm mol–2 and b = 0.1383 L mol–1, calculate compressibility factor Z under (a) low pressure region. (b) high pressure region.

Two moles of ammonia gas are enclosed in a vessel of 5 litre capacity at 27oC. Calculate the pressure exerted by the gas, assuming that (i) the gas behaves like an ideal gas (using ideal gas equation). (ii) the gas behaves like a real gas (using van der Waal's equation). Given that for ammonia, a = 4.17 atm litre2 mol–2 and b = 0.037 litre mol–1

The compressibility factor for 1 mole of a van der Waals gas at 0oC and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant, a.

The rms speed of an ideal gas at 27°C is 0.3 ms–1 . Its rms speed at 927°C (in ms–1) is

The rms speed of CO2 at a temperature T (in kelvin) is x cm s–1.At what temperature (in kelvin) the rms speed of nitrous oxide would be 4x cm s–1 ?

A sample of butane gas C4H10 of unknown mass is contained in a vessel of unknown volume V at 25oC and a pressure of 760 mmHg. To this vessel 8.6787 g of neon gas is added in such a waythat no butane is lost from the vessel. The final pressure in the vessel is 1920 mm Hg at the same temperature. Calculate the volume of the vessel and the mass of butane.

One litre flask contains air, water vapour and a small amount of liquid water at a pressure of 200 mmHg. If this is connected to another one-litre evacuated flask, what will be the final pressure of the gas mixture at equilibrium?Assume the temperature to be 50°C.Aqueous tension at 50°C = 93 mm Hg.

1 mole of N2 and 3 moles of H2 are mixed in 8.21 lit. container at 300 K to form NH3 . If at equilibrium, average molecular mass was found to be 34/3, then find partial pressure of each component.

A vessel of 2 lit. capacity contains hydrogen at 380 mm pressure at 27°C. 16 gm of O2 is added to the container at constant temperature, then find the final total pressure and final partial pressure of H2 . Sol. As partial pressure of a gas is independent from the pressure of other gas, initial as well as final partial pressue of H2 gas,

A mixture of CO and CO2 is found to have a density of 1.50 g/litre at 30oC and 730 mm. The mole percent of CO in the mixture is

The density of methane at 2.0 atmosphere pressure and 27°C is

A spherical balloon of 21 cm diameter is to be filled up with hydrogen at 0oC and 1 atm from a cylinder containing the gas at 20 atmosphere at 27oC. If the cylinder can hold 2.82 litre of water at 0oC and 1 atm, calculate the number of balloon that can be filled up.

When 3.2 g of sulphur is vapourised at 450°C and 723 mm pressure, the vapours occupy a volume of 780 ml. What is the molecular formula of sulphur vapours under these conditions?

An open vessel at 27oC is heated at constant pressure until 3/5th of the air in it has been expelled. Find (a) the temperature at which vessel was heated ? (b) the moles of air eascaped out, if vessel were heated to 900 K ? (c) temperature at which half of the air escapes out ?

In a barometeric tube Hg is replaced by H2O then find the height of H2O column to measure the atmospheric pressure.Assume that vapour pressure of H2O in negligible.

Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm, what is the depth of the lake ? The density of lake-water and Hg are 1.0 gm/ml and 13.6 gm/ml, respectively. Assume that temperature of lake water is equal to that of atmosphere.Also neglect the contribution of pressure due to surface tension.

A balloon of diameter 20 m weighs 100 kg. Calculate its paylod if it is filled with helium at 1.0 atm and 27 ∘ C. Density of air is 1.2 kg m −3 .(R=0.082 dm 3 atm K −1 mol −1 ).

Calculate payload of a balloon having volume 100 litre. It is filled with helium gas at 0.2486 atm pressureand 300K. Density of air is 1.3 gm/litre and mass of material of balloon is 20 gm.

A 10 cm column of air is trapped by a column of Hg, 8 cm long, in a capillary tube horizontally fixed as shown below, at 1 atm pressure. Calculate the length of air column when the tube is fixed at the same temperature (a) vertically with open end up (b) vertically with open end down (c) At 45° from vertical, with open end up.

What is Boltzmann's constant?

The Ideal gas law PV=nRT

Where n is number of moles of gas

              n=N/NA

Where N= number of gaseous molecules and NA is Avagadro's  number

            PV=(N/NA)×RT

            PV=N(R/NA)×T

            PV=N(Kb)×T

Where Kb is Boltzmann's constant

 Kb=R/NA= (8.31÷6.022×10^23)

                  = 1.38×10^-23

The States of matter : Numerical Questions : Part-(3):

(1) Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

(2) A gas occupied a volume of 250 ml at 700 mm Hg pressure and 25°C. What additional pressure is required to reduce the gas volume to its 4/5th value at the same temperature

(3) A sample of a given mass of a gas at a constant temperature occupies 95cm3 under a pressure of 9.962 × 104N/m2 .At the same temperature, it volume at a pressure of 10.13 × 104 N/m2 is :

(4) Calculate the mass of mercuryin a uniform column, 760 mm high and 1.00 cm2 in cross-sectional area. Is there any change in 

(a) mass and 

(b) pressure of column of same height but with 2.00 cm2 cross sectional area is taken ? (density of Hg = 13.6 g/cm3 )

(5) 1 mole of CCl4 vapours at 77oC occupies a volume of 35.0 L. If vander waal's constants are a = 20.39 L 2 atm mol–2 and b = 0.1383 L mol–1, calculate compressibility factor Z under 

(a) low pressure region. 

(b) high pressure region.

(6) Two moles of ammonia gas are enclosed in a vessel of 5 litre capacity at 27oC. Calculate the pressure exerted by the gas, assuming that 

(i) the gas behaves like an ideal gas (using ideal gas equation). 

(ii) the gas behaves like a real gas (using van der Waal's equation). Given that for ammonia, a = 4.17 atm litre2 mol–2 and b = 0.037 litre mol–1

(7) The compressibility factor for 1 mole of a van der Waals gas at 0oC and 100 atm pressure is found to be 0.5. Assuming that the volume of a gas molecule is negligible, calculate the van der Waals constant, a.

(8) The rms speed of an ideal gas at 27°C is 0.3 ms–1 . Its rms speed at 927°C (in ms–1) is

(9) The rms speed of CO2 at a temperature T (in kelvin) is x cm s–1.At what temperature (in kelvin) the rms speed of nitrous oxide would be 4x cm s–1 ?

(10) A sample of butane gas C4H10 of unknown mass is contained in a vessel of unknown volume V at 25oC and a pressure of 760 mmHg. To this vessel 8.6787 g of neon gas is added in such a waythat no butane is lost from the vessel. The final pressure in the vessel is 1920 mm Hg at the same temperature. Calculate the volume of the vessel and the mass of butane.

(11) One litre flask contains air, water vapour and a small amount of liquid water at a pressure of 200 mmHg. If this is connected to another one-litre evacuated flask, what will be the final pressure of the gas mixture at equilibrium?Assume the temperature to be 50°C.Aqueous tension at 50°C = 93 mm Hg.

(12) 1 mole of N2 and 3 moles of H2 are mixed in 8.21 lit. container at 300 K to form NH3 . If at equilibrium, average molecular mass was found to be 34/3, then find partial pressure of each component.

(13) A vessel of 2 lit. capacity contains hydrogen at 380 mm pressure at 27°C. 16 gm of O2 is added to the container at constant temperature, then find the final total pressure and final partial pressure of H2 . Sol. As partial pressure of a gas is independent from the pressure of other gas, initial as well as final partial pressue of H2 gas,

(14) A mixture of CO and CO2 is found to have a density of 1.50 g/litre at 30oC and 730 mm. The mole percent of CO in the mixture is

(15) The density of methane at 2.0 atmosphere pressure and 27°C is

(16) A spherical balloon of 21 cm diameter is to be filled up with hydrogen at 0oC and 1 atm from a cylinder containing the gas at 20 atmosphere at 27oC. If the cylinder can hold 2.82 litre of water at 0oC and 1 atm, calculate the number of balloon that can be filled up.

(17) When 3.2 g of sulphur is vapourised at 450°C and 723 mm pressure, the vapours occupy a volume of 780 ml. What is the molecular formula of sulphur vapours under these conditions?

(18) An open vessel at 27oC is heated at constant pressure until 3/5th of the air in it has been expelled. Find 

(a) the temperature at which vessel was heated ? 

(b) the moles of air eascaped out, if vessel were heated to 900 K ? 

(c) temperature at which half of the air escapes out ?

(19) In a barometeric tube Hg is replaced by H2O then find the height of H2O column to measure the atmospheric pressure.Assume that vapour pressure of H2O in negligible.

(20) Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.

(21) The diameters of a buble at the surface of a lake is 4 mm and at the bottom of the lake is 1 mm. If atmospheric pressure is 1 atm, what is the depth of the lake ? The density of lake-water and Hg are 1.0 gm/ml and 13.6 gm/ml, respectively. Assume that temperature of lake water is equal to that of atmosphere.Also neglect the contribution of pressure due to surface tension.

(22) A balloon of diameter 20 m weighs 100 kg. Calculate its paylod if it is filled with helium at 1.0 atm and 27 ∘ C. Density of air is 1.2 kg m −3 .(R=0.082 dm 3 atm K −1 mol −1 ).

(23) Calculate payload of a balloon having volume 100 litre. It is filled with helium gas at 0.2486 atm pressureand 300K. Density of air is 1.3 gm/litre and mass of material of balloon is 20 gm.

(24) A 10 cm column of air is trapped by a column of Hg, 8 cm long, in a capillary tube horizontally fixed as shown below, at 1 atm pressure. Calculate the length of air column when the tube is fixed at the same temperature (a) vertically with open end up (b) vertically with open end down (c) At 45° from vertical, with open end up.

Important reasoning Questions of "the state of matter" !!

(1) Liquid ammonia bottle is cooled before opening the seal. Explain.

The molecular speeds of gaseous molecules are analogous to those of rifle bullets; why is then odour of the gaseous molecule not detected so fast?

(2) Carbon dioxide is heavier than oxygen and nitrogen but is does not form the lower layer of the atmosphere. Explain.

(3) Out of dry air and wet air, which is heavier?

(4) Can we apply Dalton’s law of partial pressure to a mixture of carbon monoxide and oxygen?

(5) Why a bottle of liquid ammonia is cooled before opening the seal?

(6) Explain , Aerated water bottles are kept under water during summer why?

(7) Arrange the following in the increasing order of melting point of different types of crystalline solid

 (i) Covalent solid 

(ii) Metallic solid 

(iii) Molecular 

(iv) Ionic

(8) Why falling liquid drops are spherical?

(9) Why diethyl ether has higher vapour pressure than ethyl alcohol at a particular temperature?

(10) Why liquid have a definite volume but no definite shape?

(11) What are the difference between Diffusion and Effusion ?

(12) What is payload of Balloon ?

(13) What is Aqueous tension ?

(14) What is Vander waals equation of state of a real gas ?

(15) What is Boyle's temperature ? and what is relation of Boyle's temperature with Vander waal's constant?

 

Liquid ammonia bottle is cooled before opening the seal. Explain.

Liquid ammonia bottle contains the gas under very high pressure. If the bottle is opened as such, then the sudden decrease in pressure will lead to a large increase in the volume of the gas. As a result, the gas will come out of the bottle all of a sudden with force. This will lead to the breakage of the bottle and also some serious accident. However, if the bottle is cooled under tap water for sometime, this will lead to a decrease in the volume of the gas to a large extent. If the seal is opened now, the gas will come out of the bottle at a slow rate, thus, reducing the chances of accident.

The molecular speeds of gaseous molecules are analogous to those of rifle bullets; why is then odour of the gaseous molecule not detected so fast?

No, doubt molecules in the gaseous state move almost with the speed of rifle bullets. But these molecules donot follow a straight path. Since they undergo collisions with one another at a very fast rate, the path followed is zig-zag. Thus, the odour cannot be detected at the same speed at which the molecules move.

Carbon dioxide is heavier than oxygen and nitrogen but is does not form the lower layer of the atmosphere. Explain.

The diffusion of the gases is quite independent of the gravitational pull by the earth. The molecules of carbon dioxide remain distributed throughout the atmosphere. Therefore, carbon dioxide does not form the lower layer of the atmosphere.

Out of dry air and wet air, which is heavier?

Dry air mainly contains gases like nitrogen and oxygen along with small proportions of the other gases. The wet air on the other hand, also contains a small amount of water vapours. Now, vapour density of water vapours is less than that of nitrogen and oxygen because molar mass of H2O (18) is less than that of N2 (28) and O2 (32). This means that heavier molecules or nitrogen and oxygen have been replaced by lighter molecules of water vapours when the dry air changes to we air. Therefore, dry air is heavier than wet air.

Can we apply Dalton’s law of partial pressure to a mixture of carbon monoxide and oxygen?

No, the law cannot be applied because these gases readily combine to form carbon dioxide. The law can be applied only to the non reacting gases.

Why a bottle of liquid ammonia is cooled before opening the seal?

If the seal is opened without cooling, the liquid ammonia suddenly vaporises and gushes out of the bottle with force. This may lead to serious accidents.

Explain , Aerated water bottles are kept under water during summer why?

Aerated water contains CO2 dissolved in water. The solubility of gas decreases with rise in temperature. Thus, amount of free gas in bottle can increase in summer, which may result into increase in pressure and ultimately explosion. To avoid this they are kept under cold water.

Arrange the following in the increasing order of melting point of different types of crystalline solid (i) Covalent solid (ii) Metallic solid (iii) Molecular (iv) Ionic

Covalent > Ionic > Metallic > Molecular (∼ 4000 K) (∼ 1000 K) (880 -1000 K) (273- 600 K)

Why falling liquid drops are spherical?

This is due to property of surface tension possessed by the liquids.This makes the surface area minimum. For a given volume, sphere has minimum surface area.

Why diethyl ether has higher vapour pressure than ethyl alcohol at a particular temperature?

This is because the intermolecular forces of attraction in ethyl alcohol are stronger than those present in diethyl ether.

Why liquid have a definite volume but no definite shape?

This is because the intermolecular forces are strong enough to hold the molecule together but not so strong as to fix them into definite positions (as in solids) instead, they possess fluidity and hence no definite shape.

Volume of a cylinder containing 10 marbles and gas is 1 litre at 2 atm pressure. Now pressure on the cylinder is increased to 4 atm, at which volume becomes 725 ml. Calculate volume of each marble.the

A gas occupied a volume of 250 ml at 700 mm Hg pressure and 25°C. What additional pressure is required to reduce the gas volume to its 4/5th value at the same temperature

A sample of a given mass of a gas at a constant temperature occupies 95cm3 under a pressure of 9.962 × 104N/m2 .At the same temperature, it volume at a pressure of 10.13 × 104 N/m2 is :

Calculate the mass of mercuryin a uniform column, 760 mm high and 1.00 cm2 in cross-sectional area. Is there any change in (a) mass and (b) pressure of column of same height but with 2.00 cm2 cross sectional area is taken ? (density of Hg = 13.6 g/cm3 )