Simplify if possible:
Section 2.4
Find xas a function of y:
23.y 1 = 1 x 1 − 12 24. 25. 26.
Fory 1 = 1 f(x), (i)find xas a function of y, (ii)sketch graphs ofy 1 = 1 f(x)andx 1 = 1 f
− 1
(y):
30.y
2
1 = 1 x
2
1 + 11 31.y 1 = 1 (x
2
1 − 1 1)
2
32.The virial equation of state of a gas can be approximated at low pressure as
where pis the pressure,V
mis the molar volume, Tis the temperature, Ris the gas
constant, and Bis the second virial coefficient. Express Bas an explicit function of the
other variables.
33.Kohlrausch’s law for the molar conductivityΛ
mof a strong electrolyte at low
concentration cis
whereΛ
0
mis the molar conductivity at infinite dilution and Kis a constant. Express cas
an explicit function ofΛ
m.
34.The Langmuir adsorption isotherm
gives the fractional coverage θof a surface by adsorbed gas at pressure p, where Kis a
constant. Express pin terms of θ.
35.In Example 2.12 on the van der Waals equation, verify the explicit expressions given for
Tand p, and the cubic equation in V.
Section 2.5
Expand (write out in full):
Find the equation and sketch the graph of the straight line that passes through the points:
40.(−2, −5) and (1, 4) 41.(−1, 6) and (3, −2)
nx
nn!
20
3
=
∑
kk x
kk()+
−
=
∑
1
1
3
ix
ii−
=
∑
1
0
3
()nx
nn=
∑
1
0
2
θ=
Kp
1 Kp
ΛΛ
mm=−
0
K c
pV RT
B
V
mm=+
1
y
x
x
=
−
2
2
1
1
y
x
x
=
−
1
21
y
x
x
=
−
23
32
y
x
x
=
1 −
yx=−
1
3
2( )
yx=+1
2
() 31
231
32
2
2
xx
xx
−+
−+
x
xx
2
2
9
56
−
++
xx
x
2
32
2
++
x
x
2
4
2
−
−
x
x
2
4
x
32 xx
2
2.9 Exercises 59