Question 17.1: Using the concentration data provided in Table 17.2, determi...
Using the concentration data provided in Table 17.2, determine the membrane potential in human cells of sodium, potassium, and chlorine ions at 37.0°C.
| Table 17.2 Approximate Ion Concentration Inside and Outside Human Cells | ||
| Ion | Concentration in Osmoles per cm³ of Water | |
| Outside the Cell | Inside the Cell | |
| \text{Na}^+ | 144 | 14.0 |
| \text{K}^+ | 4.1 | 140 |
| \text{Mg}^{2+} | 1.5 | 31 |
| \text{Cl}^– | 107 | 4.00 |
| \text{HCO}_3^− | 27.7 | 10.0 |
| \text{SO}_4^{2−} | 0.5 | 1 |
| \text{HPO}_4^{2−} , \text{H}_2\text{PO}_4^− | 2.0 | 11 |
| Note: One osmole is the number of gram moles of the substance that do not diffuse or dissociate in solution. Also, \text{pH}_\text{outside} = 7.4 and \text{pH}_\text{inside} = 7.0, where the concentration of hydrogen ions (\text{H}^+) in gmoles/L is 10^{−pH}. | ||
Table 17.2 gives the concentration of sodium ions inside a human cell at 37.0°C as
c_{\text{Na}_c^+} = 14.0 \text{osmoles/cm}^3
while the concentration of sodium ions outside the cell is
c_{\text{Na}_o^+} = 144 \text{osmoles/cm}^3
The valence of a sodium ion is 1 \text{kgmole electrons/kgmole Na}^+. Then, Eq. (17.9) gives the membrane potential of sodium as
E_i( \text{at} 37°\text{C}) = \frac{[8314.3 \text{J/(kgmole.K)}] (37.0 + 273.15 \text{K}))}{z_i(96,487 \text{kilocoulombs/kgmole)}} \text{ln} (\frac{c_{io}}{c_{ic}})
= \frac{26.7 \text{millivolts.(kgmole electrons/kgmole} i)}{z_i} \text{ln} (\frac{c_{io}}{c_{ic}}) (17.9)
\text{E}_{\text{Na}_c^+} = \frac{26.7 \text{mV(kgmole electrons/kgmole Na}^+)}{z_{\text{Na}^+} \text{kgmole electrons/kgmole Na}^+} \text{ln} (\frac{c_{\text{Na}_o^+}}{c_{\text{Na}_c^+}})
= \frac{26.7 \text{mV(kgmole electrons/kgmole Na}^+)}{1 \text{kgmole electrons/kgmole Na}^+} \text{ln}(\frac{144}{14.0}) = 62.2 \text{mV}
For potassium, Table 17.2 gives c_{K_c^+} = 140 \text{osmoles/cm}^3 and c_{K_o^+} = 4.1 \text{osmoles/cm}^3. The valence of a potassium ion is also 1 \text{kgmole electrons/kgmole K}^+ , and Eq. (17.9) gives the membrane potential of potassium in a human cell as
E_{K^+} = \frac{26.7 \text{mV(kgmole electrons/kgmole K}^+)}{1 \text{kgmole electrons/kgmole K}^+} \text{ln} \frac{4.1}{140} = – 94.3 \text{mV}
Finally, Table 17.2 gives c_{Cl_c^−} = 4.00 \text{osmoles/cm}^3 and c_{Cl_o^− } = 107 \text{osmoles/cm}^3. The valence of a chlorine ion is –1 \text{kgmole electrons/kgmole Cl}^– , and Eq. (17.9) gives the membrane potential of chlorine in a human cell as
E_{Cl^-} = \frac{26.7 \text{mV(kgmole electrons/kgmole Cl}^-)}{1 \text{kgmole electrons/kgmole Cl}^-} \text{ln} \frac{107}{4.00} = −87.8 \text{mV}