Question

(a) Calculate the free energy needed to move. 1 mole of sodium ions from the plasma

where [Na] = 150 mM, into the red blood cell where [Na] = 5 mM assuming a
membrane potential of -70 mV at 37°C (R = 1.98 cal.mol-¹.K-¹ and
F = 23062 cal.V1¹.mol-¹).
[12 marks]
(b) If this process is 41% efficient, how many moles of ATP can be synthesized when
coupled to such an influx of ions? (Hydrolysis of 1 mole of ATP releases 7.3 kilo
calories of energy).
[8 marks]

Answer 1

To calculate the free energy needed to move 1 mole of sodium ions from the plasma to the red blood cell, we can use the Nernst equation. The valence of sodium ions is 1, so Z = 1. The free energy can be calculated using the equation G = -nF E, where n is the number of moles of ions and F is the Faraday constant.

Step-by-step explanation:

To calculate the free energy needed to move 1 mole of sodium ions from the plasma to the red blood cell, we can use the Nernst equation which relates the concentration gradient and the membrane potential. The equation is given as:

E = (RT/ZF) * ln([Na]out/[Na]in)

Where E is the membrane potential, R is the gas constant, T is the temperature in Kelvin, Z is the valence of the ion, F is the Faraday constant, [Na]out is the concentration of sodium ions outside the cell, and [Na]in is the concentration of sodium ions inside the cell.

Plugging in the values:

• E = -70 mV = -70 * (1/1000) V
• R = 1.98 cal.mol-1.K-1
• F = 23062 cal.V-1.mol-1
• T = 37 + 273 K = 310 K
• [Na]out = 150 mM = 150 * (1/1000) mol/L
• [Na]in = 5 mM = 5 * (1/1000) mol/L

Plugging these values into the equation:

E = (1.98 * 310 / Z * 23062) * ln(150/5)

The valence of sodium ions is 1, so Z = 1.

Now we can calculate the value of E and convert it to free energy using the equation:

G = -nF E

Where n is the number of moles of ions and F is the Faraday constant.

In this case, n = 1 mole and F = 23062 cal.V-1.mol-1.

Substituting the values:

G = -1 * 23062 * E

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