3rd chapter exersise short question - 1st year chemistry

(b)   What is the physical significance of van der Waals constant, ‘a’ and ‘b’.

Give their units.

Ans.    (b)       Physical Significance of van der Waals constant ‘a’ and ‘b’

            (i)         Significance of’ a’:    The value of constant ‘a’ is a measure of the intermolecular attractive forces and greater will be the ease of its liquefaction.

            Units of ‘a’ :

                        The units of ‘a’ are related to the units of pressure, volume and number of moles.

P=             or        

a= =

a= atm dm⁶ mol^-2

            In SI units:                  a= ==Nm⁴ mole ^-2

(iii)             Significance of ‘b’: The value of constant ‘b’ us related to the size of the molecule. Larger the size of the molecule, lager is the value of ‘b’. It is effective volume of the gas molecules.

Units of ‘b’:   

‘b’ is the  compressible volume per mole of gas. So the units of ‘b’ are related to the units of volume and moles.

V=nb      or         b =

b==dm³ mol^-1

   In SI units:      b===dm³ mol^-1 

 Q. Do you think that 1 mole of H₂ and 1 mole NH₃ at 0^oC and 1 atm pressure will have equal Avogadro’s number of particles? If not, why?

 Justify that 1 cm³ of H₂ and 1 cm³ of CH₄ at STP will have the same number of molecules, when one molecules of CH₄ is 8 times heavier than that of hydrogen.

Ans     1 mole of H₂ and 1 mole of NH₃ at 0^oC and 1 atm pressure will have equal number of molecules under the same conditions of temperature and pressure. Hence, 1 cm3 of H2 and 1 cm3 of CH4 at STP will have the same number of molecules.

Q15.    Explain the following  facts:

(a)   The plot of PV versus P is a straight line at constant temperature and with a fixed number of moles of an ideal gas.
ans:
 At constant temperature and with a fixed number of moles of an ideal gas, when the pressure of the gas is varied, its volume changes, but the product PV remains constant. Thus,

            P₁ V₁ =  P₂ V₂ = P₃ V₃ =

            Hence, for any fixed temperature, the product PV when plotted against P.a straight line parallel to P-axis is obtained. This straight line indicates that PV remains constant quantity.

(b)  The straight line in (a) is parallel to pressure-axis and goes away from the pressure axis at higher pressure for many gases.
ans:

Now, increase the temperature of the same from T₁ to T₂ .At

constant temperature T₂ and with the same fixed number of moles

of an ideal gas, when the constant. However, the value of PV

increase with increase in temperature. On plotting graph between P

on x-axis is obtained. This  straight line at T₂ will be away from the

x-axis. This straight line also shows that PV is a constant quantity.

(c)   The van der walls constant ‘b’ of a gas is four times the molar volume of that gas
    Excluded volume, ‘b’ is four times the molar volume fo gas. The excluding with each other as shown in Fig. The spheres are considered to be non-compressible. So the molecules cannot approach each other more closely than the distance, 2r . Therefore, the space indicated by the dotted sphere having radius, 2r will not be available to all other molecules of the gas. In other words, the dotted spherical space is excluded volume per pair of molecules.

                        Let each molecules be a sphere with radius   =r

                        Volume of one molecules (volume of sphere)= 

            The distance of the closest approach of 2 molecules =2 r

                        The excluded volume for 2 molecules=

                        The excluded volume for 1 molecule=

                                                                              =

                                                                                    =4V_m =b

                        The excluded volume for ‘n’ molecules=n b

            Where V_m is the actual volume of a molecule.

            Hence, the excluded volume or co-volume or non-compressible volume is equal to 4 times the actual volume of the molecules of the gas.

(d)      Pressure of NH₃ gas at given conditions (say 1 atm pressure and room temperature) is less as calculated by van der Waals equation than that calculated by general gas equation.
ans:

The pressure of NH₃ calculated by general gas equation is high

because it is considered as an ideal gas. In an ideal gas, the

molecules do not exert any force of attraction on one another. On

the other hand, when the pressure of NH₃ is considered as a real

gas. Actually, NH₃ is a real gas. It consists of polar NH3 molecules

approaches the walls of the container, it experiences an inward

pull. Clearly, the molecule strikes the wall with a lesser force than

it would have done it these are no attractive forces. As a result  of

this , the real gas pressure is less than the ideal pressure.

(e)   Water vapors do not behave ideally at 273 k.
 ans:
    Water vapors present at 273K do not behave ideally because polar       

water molecules exert force of attraction on one another.

(f)  SO₂ is comparatively non-ideal at 273 k but behaves ideally at 327 K.
ans:
At low temperature, the molecules of SO2 possess low kinetic energy. They come close to each other. The e intermolecular attractive forces become very high. So, it behave non-ideally at 273K. At high temperature, the molecules of SO2 have high kinetic energy. The molecules are at larger distances from one other another. The intermolecular attractive forces become very weak. So, it behaves ideally at 327K.