Question

Upon fertilization, the eggs of many species undergo a rapid change in potential difference across their outer membrane. This change affects the physiological development of the eggs. The potential difference across the membrane is called the membrane potential, Vm, which is the potential inside the membrane minus the potential outside it. The membrane potential arises when enzymes use the energy available in ATP to expel three sodium ions (Na+) actively and accumulate two potassium ions (K+) inside the membranemaking the interior less positively charged than the exterior. The egg membrane behaves as a capacitor with a capacitance of about 1 μF/cm2. The concentration of Na+ is about 30 mmol/L in the eggs interior but 450 mmol/L in the surrounding seawater. The K+ concentration is about 200 mmol/L inside but 10 mmol/L outside. A useful constant that connects electrical and chemical units is the Faraday number, which has a value of approximately 105 C/mol; that is, Avogadros number (a mole) of monovalent ions, such as Na+ or K+, carries a charge of 105 C.
How many moles of Na+ must move per unit area of membrane to change Vm from -70 mV to +30 mV , if we assume that the membrane behaves purely as a capacitor?

10−4 mol/cm2
10−9 mol/cm2
10−12 mol/cm2
10−14 mol/cm2

Answer 1

Answer:

the correct option is 3 = 10−12 mol/cm2 moles of Na+ must move per unit area of membrane.

Explanation:

The capacitance is given by ;

• C = Q/V

the specific capacitance ;

• C/A = (Q/A)/V where A is the area

it is said that the potential changes from -70 mV to +30 mV

• hence potential difference is ; V = +30 mV - ( -70 mV)

= 100mV

The charge moving per unit area;

• Q/A = V(C/A)

= 100mV X 10^-3V/1mV X 1microF X 10^-6F/1microF

= 1 X 10^-7C/m^2

• Hence the number of moles moving per unit area ;

• n = Q/A/faraday number

• = 1 X 10^-7 C/m^2/10^5C/mol

= 10^-12mol/cm^2

As such, the correct option is 3 = 10−12 mol/cm2  moles of Na+ must move per unit area of membrane.