Calculate the viscosity coefficient of O2 gas at 292K from its hard-sphere diameter. Compare your result with the value in Table A.18 in the appendix.

Question

Calculate the viscosity coefficient of [latex]O_{2}[/latex] gas at 292K from its hard-sphere diameter. Compare your result with the value in Table A.18 in the appendix.

Table A.18 Coefficients of Viscosity
Substance	State	Temperature/°C	[latex]η×10^{3}/kgm^{−1} s^{−1}[/latex]
Benzene	Liquid	20	0.652
Carbon tetrachloride	Liquid	20	0.969
Ethanol	Liquid	20	1.2
		40	0.834
Glycerol	Liquid	0	12, 110
		20	1490
Hexane	Liquid	0	0.401
		20	0.326
Mercury	Liquid	0	1.685
		20	1.554
Sulfuric acid	Liquid	20	25.4
Water	Liquid	0	1.787
		20	1.002
		25	0.8904
		100	0.2818
Argon	Gas	0	0.02096
		20	0.02217
Carbon dioxide	Gas	0	0.0139
		20	0.0148
Helium	Gas	20	0.01941
		100	0.02281
Nitrogen	Gas	27.4	0.01781
		127.2	0.02191
Oxygen	Gas	0	0.0189
		19.1	0.02018
Water	Gas	100	0.01255
		200	0.01635
From R. C.Weast, ed., Handbook of Chemistry and Physics, 64th ed., CRC Press, Boca Raton, FL, 1983,p. F38ff.

Accepted Answer

[latex] m=\frac{0.03200 kg mol^{−1}}{6.02214 × 1023 mol^{−1}} =5.3137 × 10^{−26} kg[/latex]

[latex]η=\frac{5}{16} \frac{1}{(3.58×10^{−10} m)^{2}} \Bigl(\frac{(5.3137×10^{−26} kg)(1.3807×10^{−23} J K^{−1})(292 K)}{π} \Bigr)^{1/2}[/latex]

[latex]=2.013×10^{−5} kg m^{−1} s^{−1}[/latex]

The value in Table A.18 is [latex]2.018 g×10^{−5} kg m^{−1} s^{−1}.[/latex] This relatively close agreement is not surprising since the effective hard-sphere diameters are presumably obtained from viscosity data, probably using a somewhat more accurate formula than [latex] Eq. (10.3-12): η=\frac{5π}{32} mλ\left\langle v \right\rangle N=\frac{5}{16} \frac{1}{d^{2}}\sqrt{\frac{mk_{B}T}{π} } . [/latex]

Table A.18 Coefficients of Viscosity
Substance	State	Temperature/°C	[latex]η×10^{3}/kgm^{−1} s^{−1}[/latex]
Benzene	Liquid	20	0.652
Carbon tetrachloride	Liquid	20	0.969
Ethanol	Liquid	20	1.200
		40	0.834
Glycerol	Liquid	0	12, 110
		20	1490
Hexane	Liquid	0	0.401
		20	0.326
Mercury	Liquid	0	1.685
		20	1.554
Sulfuric acid	Liquid	20	25.4
Water	Liquid	0	1.787
		20	1.002
		25	0.8904
		100	0.2818
Argon	Gas	0	0.02096
		20	0.02217
Carbon dioxide	Gas	0	0.01390
		20	0.01480
Helium	Gas	20	0.01941
		100	0.02281
Nitrogen	Gas	27.4	0.01781
		127.2	0.02191
Oxygen	Gas	0	0.0189
		19.1	0.02018
Water	Gas	100	0.01255
		200	0.01635
From R. C.Weast, ed., Handbook of Chemistry and Physics, 64th ed., CRC Press, Boca Raton, FL, 1983,p. F38ff.

Question 10.14: Calculate the viscosity coefficient of O2 gas at 292K from i...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions