Question 9.7.1: The Activity Coefficient of Hemoglobin The following data ar...

The Activity Coefficient of Hemoglobin

The following data are available on the activity of hemoglobin in aqueous solution.^{18}

c (g/L) a (g/L) c (g/L) a (g/L) c (g/L) a (g/L)
20 23.1 120 330 220 2060
40 53.5 140 473 240 3040
60 94.6 160 679 260 4580
80 150 180 973 280 7040
100 226 200 1410 300 11050

Compute the hemoglobin activity coefficient as a function of concentration, and fit those results using Eq. 9.7-21.

\ln \gamma_{ i }^{\bullet}=B_{i} \cdot c_{i}+C_{ i } \cdot c_{i}^{2}+D_{i} \cdot c_{i}^{3}+\cdots (9.7-21)

^{18}A. P. Minton, J. Molec. Biol. 110, 89 (1977).

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It is the activity coefficients, rather than the activities, that should be fit. So the first step is to calculate the activity coefficient at each concentration from \gamma(c)=a(c) / c. The result is

 

c (g/L) \gamma^{\bullet} c (g/L) \gamma^{\bullet} c (g/L) \gamma^{\bullet}
20 1.155 120 2.750 220 9.364
40 1.337 140 3.379 240 12.67
60 1.577 160 4.244 260 17.62
80 1.875 180 5.406 280 25.14
100 2.260 200 7.050 300 36.83

 

We find that the equation

 

\ln \gamma_{ i }^{\bullet}=7.139 \times 10^{-3} \cdot c _{ i }+6.940 \times 10^{-6} \cdot c _{ i }^{2}+3.116 \times 10^{-8} \cdot c _{ i }^{3}

 

provides a good fit to the activity coefficients, as shown in the figure below.

The activity coefficients of hemoglobin as a function of concentration. The line is the fit of Eq. 9.5-24, and the points • are the reported data.

9.7.1

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