Calculate the free energy change (ΔG transport) for the movement of Na + into a cell when its concentration outside is 150 mM and its cytosolic concentration is 10 mM. Assume that T = 20°C and ΔΨ = –50 mV (inside negative).
A
–1.7 KJ/mol.
B
–11.4 KJ/mol.
C
–11,600 KJ/mol.
D
11.4 KJ/mol.
E
14.3 KJ/mol.
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1
Start by understanding the formula for calculating the free energy change (ΔG_transport) for ion movement across a membrane: ΔG_transport = RT ln([Na⁺]_inside/[Na⁺]_outside) + zFΔΨ.
Identify the variables: R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, z is the charge of the ion (for Na⁺, z = +1), F is Faraday's constant (96485 C/mol), and ΔΨ is the membrane potential difference.
Convert the temperature from Celsius to Kelvin: T = 20°C + 273.15 = 293.15 K.
Calculate the first term: RT ln([Na⁺]_inside/[Na⁺]_outside). Substitute the values: R = 8.314 J/mol·K, T = 293.15 K, [Na⁺]_inside = 10 mM, [Na⁺]_outside = 150 mM. Use the natural logarithm function.
Calculate the second term: zFΔΨ. Substitute the values: z = +1, F = 96485 C/mol, ΔΨ = -50 mV (convert mV to V by dividing by 1000). Combine both terms to find ΔG_transport.