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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 505
E14C.2(b) �e height climbed by a liquid in a capillary tube of radius r is given by [14C.8–
607], h = 2γ/ρgaccr, assuming that the contact angle is zero. Rearranging for
γ, replacing r by 12d where d is the diameter of the tube, and noting that 1 N =
1 kgms−2 gives
γ = 1
2 ρgaccrh = 1
4 ρgaccdh
= 1
4 (0.9956 × 10
3 kgm−3)×(9.807ms−2)×(0.320 × 10−3 m)
×(9.11 × 10−2 m) = 0.0711... kg s−2 = 71.2 mNm−1
E14C.3(b) �e pressure di�erence between the inside and outside of a spherical droplet is
given by the Laplace equation [14C.7–606], pin = pout + 2γ/r. Hence, noting
that 1 Pa = 1 Nm−2,
∆p = pin − pout =
2γ
r
= 2 × (22.39 × 10−3 Nm−1)
(220 × 10−9 m)
= 204 kPa
E14C.4(b) �e height climbed by a liquid in a capillary tube of radius r is given by [14C.8–
607], h = 2γ/ρgaccr, assuming that the contact angle is zero. Rearranging for γ
and noting that 1 N = 1 kgms−2 gives
γ = 1
2 ρgaccrh
= 1
2 ×(0.9500×10
3 kgm−3)×(9.807ms−2)×(0.300×10−3 m)
×(10.00×10−2 m) = 0.139... kg s−2 = 139.7 mNm−1
Solutions to problems
P14C.2 �e dependence of the surface tension on surfactant concentration is given by
[14C.14–610], (∂γ/∂ ln[c/c−○])T = −RTΓS.�is equation implies that a plot of γ
against ln(c/c−○) has a slope equal to −RTΓS.�e data are plotted in Fig. 14.13.
[A]/moldm−3 ln([A]/c−○) γ/Nm−1
0.10 −2.303 0.070 2
0.20 −1.609 0.067 7
0.30 −1.204 0.065 1
0.40 −0.916 0.062 8
0.50 −0.693 0.059 8
�e points appear to lie on a curve rather than a straight line, indicating that ΓS
is not constant over this range of concentration. �e data are a good �t to the
quadratic
(γ/Nm−1) = −0.003288 × [ln([A]/c−○)]2 − 0.01614 × ln([A]/c−○) + 0.05042