Physical Chemistry Third Edition

10.4 Transport Processes in Liquids 473

Equation (10.4-4) allows us to expressfin terms ofD 2 , the diffusion coefficient

of the macromolecular substance, giving

M 2 

RTS

D 2 ( 1 −ρ 1 /ρ 2 )

(10.4-13)

where we have replacedkBNAvby the ideal gas constantR. This equation has been

widely used to obtain molar masses of proteins. It is possible to get values of bothSand

D 2 from the same experiment if a concentration profile similar to that of Figure 10.4

can be observed.

EXAMPLE10.19

The sedimentation coefficient of a sample of human hemoglobin in water is equal to 4.48

svedberg at 20◦C, and its density is 1.335 g mL−^1. The density of water at this temperature

is equal to 0.998 g mL−^1. Use the value of the diffusion coefficient from Example 10.16 to

determine the molar mass of hemoglobin.

Solution

M

(

8 .3145 J K−^1 mol−^1

)

( 293 .15 K)

(

4. 48 × 10 −^13 s

)

(

6. 9 × 10 −^11 m^2 s−^1

)(

1 −

0. 998

1. 335

)

63 J m−^2 s^2 mol−^1 63 kg mol−^1

The actual molar mass is 68 kg mol−^1.

Exercise 10.17

Assume that an ultracentrifuge rotor is rotating at 1. 00 × 105 revolutions per second and that

hemoglobin molecules in aqueous solution at 20◦C are 12.0 cm from the axis of rotation.

a.Find the sedimentation speed. Find the mean distance sedimented by the molecules in

10.0 minutes.

b.Find the root-mean-square distance in one direction diffused by hemoglobin molecules in

this temperature in 10.00 minutes.

PROBLEMS

Section 10.4: Transport Processes in Liquids

10.34A lead BB (a spherical projectile) is falling at a steady
speed in glycerol at 20◦C. Find its speed. The diameter of
the BB is 0.177 inch, and the density of lead is
11.35 g cm−^3.

10.35The following are data for the viscosity of benzene, with

the viscosity in centipoise (1 poise1gcm−^1 s−^1 ).

T/K 273. 15 283. 15 293. 15 303. 15 313. 15

η/cP 0. 912 0. 758 0. 652 0. 564 0. 503

T/K 323. 15 333. 15 343. 15 353. 15

η/cP 0. 442 0. 392 0. 358 0. 329