The potassium-ion concentration in blood plasma is about 5.0⨉10^-3 M, whereas the concentration in muscle-cell fluid is much greater (0.15 M ). The plasma and intracellular fluid are separated by the cell membrane, which we assume is permeable only to K⁺. (a) What is ΔG for the transfer of 1 mol of K⁺ from blood plasma to the cellular fluid at body temperature 37 °C? (b) What is the minimum amount of work that must be used to transfer this K⁺?

Video transcript

Hello. Everyone in this video we're calculating for the delta G. At 37 degrees Celsius for the transfer of one mole of any plus from the blood plasma to the intracellular fluid plus first go ahead and write out the reaction. So on the starting material side we have our an A. Plus guardian of the plasma. And then on my product side I have the N. A. Plus Canadians from the intro cellular fluid. Alright, so both fluids are agrees on both sides of the cell membrane. Let's go ahead and assume that R. K. Value is equal to exactly one, which then therefore tells me that my delta G is equal to zero. So now calculating for my delta G. Let's recall that delta G is equal to delta G. Not plus R. O. T. Multiplied by the natural log of Q. Sir, value Q. Here is equal to the concentration of RNA plus from our intracellular fluid over the concentration of R. N. A. Plus from the plasma. So, plugging in my numerical values then We have 0.012 on top and 0.137 as my denominator. Putting that into my calculator, I will get that my Q value is equal to 0.08759. All right, so far as for my temperature, I'm gonna want to convert this into kelvin's. We have this currently at 37 degrees Celsius. I'll go ahead and add 273.15 to convert my Celsius units into kelvin. So I have these two numbers up we get 3 10.15 kelvin's. So now we can successfully plug in all the values for this equation, leaving us with delta G equaling to zero plus 8.314 units being jewels over Mold Times, Kelvin Multiplied by 310. Kelvin multiplied by the natural log of 0.08759. So once I put that in to my calculator I'll get them my delta G equals equals to negative 6 to jules. We want this to be in units of killer jewels. So we do a simple direct conversion. So for every 1000 jewels we have one kill a jewel again, putting this value or these calculations into my calculator, I'll get my final answer of delta G. Equaling to negative 6.3 kg jewels. And this right here is going to be my final answer for this problem. Thank you all so much for watching