Calculate the work required to transfer 1 mol of
K+ from the blood to muscle cells?

Question

Potassium ions are moved across cell membranes by “ion pumps,” which
make it possible for the cell to expend energy needed to maintain different
concentrations of ions on either side of the membrane. In humans, the
concentration of potassium ions in the blood is 5.0x10-3 M, while the concentration
inside of muscle cells is 0.15M. Calculate the work required to transfer 1 mol of
K+ from the blood to muscle cells.

Daniel Arnold · Accepted Answer

The work required is 0.09 kJ.

An example of a common formula for ion transfer energy is #color(blue)(bar(ul(|color(white)(a/a) ΔG = RTln(["K"^(+)]_text(in)/["K"^(+)]_text(out)) + ZFΔψ color(white)(a/a)|)))# where #ΔG# = the free energy change #R# = the Ideal Gas Law Constant #T# = the temperature #["K"^(+)]_text(in)# and #["K"^(+)]_text(out)# are the potassium ion concentrations inside and outside the cell #Z# = the charge on the ion #F# = the Faraday constant #Δψ# = the membrane potential The energy required to cross the concentration gradient is represented by the first term in the expression. The energy required to traverse the electrical gradient is represented by the second term (the membrane potential). In a typical skeletal muscle cell, the membrane potential for #"K"^"+"# ions is -90 mV. The negative symbol denotes a negative internal potential in relation to the extracellular fluid around the cell. In this issue, #R = 8.314 × 10^"-3" color(white)(l)"kJ·K"^"-1""mol"^"-1"# #T = "37 °C" = "310.15 K"# #["K"^(+)]_text(in) = "0.15 mol/L"# #["K"^(+)]_text(out) = 5.0 × 10^"-3"color(white)(l) "mol/L"# #Z = +1# #F = "96 485 C·mol"^"-1" = "96.485 kJ·V"^"-1""mol"^"-1"# #Δψ = "-90 mV" = "-0.090 V"# #ΔG = RTln(["K"^(+)]_text(in)/["K"^(+)]_text(out)) + ZFΔψ# #= 8.314 × 10^"-3"color(white)(l) "kJ"·color(red)(cancel(color(black)("K"^"-1")))·"mol"^"-1"× 310.15 color(red)(cancel(color(black)("K"))) × ln((0.15 color(red)(cancel(color(black)("mol/L"))))/(5.0 × 10^"-3" color(red)(cancel(color(black)("mol/L"))))) + (+1)( "96.485 kJ"·color(red)(cancel(color(black)("V"^"-1")))"mol"^"-1")(-0.090 color(red)(cancel(color(black)("V"))))# #= 2.443ln30 "kJ·mol"^"-1" - "6.75 kJ·mol"^"-1"# #= "(8.77 - 8.68) kJ·mol"^"-1"# #= "0.09 kJ·mol"^"-1"# It will take 0.09 kJ to transfer 1 mol of potassium ions. The delivery of potassium ions to the muscle under the given circumstances is nearly energetically neutral.

Ivy Acosta · Answer

undefined The work required to transfer 1 mol of K+ from the blood to muscle cells depends on various factors such as concentration gradients, membrane potentials, and the presence of transport proteins. Without specific values for these parameters, it's not possible to provide a precise calculation. However, the work can be calculated using thermodynamic principles such as the change in free energy (∆G) associated with the transfer process.

Ruby Armstrong · Answer

undefined To calculate the work required to transfer 1 mol of K+ from the blood to muscle cells, you would need to consider the concentration gradient of K+ between the blood and the muscle cells, as well as the electrochemical potential difference across the cell membrane. The work required would be given by the equation:

$$ \text{Work} = \text{Force} \times \text{Distance} $$

where the force would be the electrochemical potential difference and the distance would be the distance across which the K+ ions are transferred.

You would need specific values for the concentration gradient and electrochemical potential difference to calculate the work accurately.

Calculate the work required to transfer 1 mol of K+ from the blood to muscle cells?