Find out the units and dimensions of the constants a and b in the vander waal.s equation `( P + ( a )/(V ^(2)))(V -b) =RT.`
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We can add and subtract only like quantities. `implies` Dimensions of P = Dimensions of `(a)/( V^(2))` ...(i) and Dimensions of v = Dimensions of b ….(ii) From (i), Dimensions of a = Dimensions of `P xx` Dimensions of `V^(2)` `[a] = [M^(1) L^(-1) T^(-2)] xx [L^(3)]^(2) = [M^(1) L^(5) T^(-2)]` Unit of a = Unit of `p xx` Unit of `v^(2) = (N)/(M^(2)) xx m^(6) = N m^(4)` From (ii) , `[b] = [ V] = M^(0) L^(3) T^(0) ]` So unit of b = Unit of `V = m^(3)`
What do the constants a and b signify in van der Waals' equation ?
In the Van der Waals equation (P + (a)/(V^(2)))(V-b) = constant, the unit of a is
The van der Waal equation of gas is (P + (n^(2)a)/(V^(2))) (V - nb) = nRT
The units of constant b used in van der Waals' equation are ………….. .
Write the units of van der Waals' constant 'a' and 'b'.
The ratio of units of van der Waals constants a and b is
For real gases, the relation between P, V and T is given by an van der Waals equation, (P+(an^(2))/(V^(2)))(V-nb)=nRT . For the following gases CH_(4),CO_(2), O_(2),H_(2) which gas will have (i) highest value of 'a' and (ii) lowest value of 'b' respectively?
The ratio a/b (the terms used in van der Waals' equation) has the unit .
At a particular temperature and pressure for a real gas Van der Waal's equation can be written as: (P + a/(V^(2)m)) (V_(m) -b) =RT where Vm is molar volume of gas. This is cubic equation in the variable Vm and therefore for any single value of P & T there should be 3 values of Vm. Which are shown in graph as Q, M and L. As temperature is made to increase at a certain higher temperature the three values of Vm becomes identical. The temperature, pressure & molar volume at point X are called Tc, Pc & Vc for real gas. The compressibility factor in terms of Pc, Vc and T is called Zc. The expression of Van dcr Waal's constant 'a' can be given as
