Estimate the diffusivity of phenol in ethanol at 20ºC (293 K).

Question

Estimate the diffusivity of phenol in ethanol at [latex]20^{\circ} C[/latex] (293 K).

Accepted Answer

Viscosity of ethanol at [latex]20^{\circ} C , 1.2 mNs / m ^{2}[/latex].

Molecular mass, 46.

Molar volume of phenol

Atom	Vol.		No. of
C	0.0148	x	6	=	0.0888
H	0.0037	x	6	=	0.0222
O	0.0074	x	1	=	0.0074
ring	-0.015	x	1	=	-0.015
					[latex]0.1034 m ^{3} / k mol[/latex]

[latex]D_{L}=\frac{1.173 imes 10^{-13}(1.5 imes 46)^{0.5} 293}{1.2 imes 0.1034^{0.6}}=\underline{\underline{9.28 imes 10^{-10} m ^{2} / s }}[/latex] (8.22)

[latex] ext { Experimental value, } 8 imes 10^{-10} m ^{2} / s[/latex]

Table 8.6. Structural contributions to molar volumes, [latex]m ^{3} / kmol[/latex] (Gambil, 1958)
Molecular volumes
Air	0.0299	[latex]CO _{2}[/latex]	0.0340	[latex]H _{2} S[/latex]	0.0329	NO	0.0236
[latex]Br _{2}[/latex]	0.0532	COS	0.0515	[latex]I _{2}[/latex]	0.0715	[latex]N _{2} O[/latex]	0.0364
[latex]Cl _{2}[/latex]	0.0484	[latex]H _{2}[/latex]	0.0143	[latex]N _{2}[/latex]	0.0312	[latex]O _{2}[/latex]	0.0256
CO	0.0307	[latex]H _{2} O[/latex]	0.0189	[latex]NH _{3}[/latex]	0.0258	[latex]SO _{2}[/latex]	0.0448
Atomic volumes
As	0.0305	F	0.0087	P	0.0270	Sn	0.0423
Br	0.0480	Ge	0.0345	Pb	0.0480	Ti	0.0357
CO	0.0270	H	0.0037	S	0.0256	V	0.0320
Cr	0.0148	Hg	0.0190	Sb	0.0342	Zn	0.0204
	0.0274	I	0.037	Si	0.0320

Cl, terminal, as in RCl	0.0216	in higher esters, ethers	0.0110
[latex] ext { medial, as in } R - CHCl - R[/latex]	0.0246	in acids	0.0120
Nitrogen, double-bonded	0.0156	in union with S, P, N	0.0083
triply bonded, as in nitriles	0.0162	three-membered ring	-0.0060
[latex] ext { in primary amines, } RNH _{2}[/latex]	0.0105	four-membered ring	-0.0085
[latex] ext { in secondary amines, } R _{2} NH[/latex]	0.012	five-membered ring	-0.0115
[latex] ext { in tertiary amines, } R _{3} N[/latex]	0.0108	six-membered ring as in benzene, cyclohexane, pyridine	-0.0150
Oxygen, except as noted below	0.0074
in methyl esters	0.0091	Naphthalene ring	-0.0300
in methyl ethers	0.0099	Anthracene ring	-0.0475

Question 8.12: Estimate the diffusivity of phenol in ethanol at 20ºC (293 K...

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