Really the most useful equations(the ones you really want to understand ) With these you can solve almost all the problems we will throw at you about osmosis. Things to remem ber though 1. Be careful with the signs! Draw a diagram with which direction you are defining flux and be consistent. (the equations written here are only if you define the flux the way I've drawn it 2. Check you unit!(always very helpfuL.) 3. Before starting the mathy part of the problem, stop and think about what will happen. Will the volume increase or decrease? At equilibrium, what will the concentrations of solutes have to be? 4. Once you finish all the math, check again to make sure that your answer makes sens Time behavior of volume in osmosis problem Plugging in from the equations above =-124((0)=c(p-x1)-(12-x2) but you also know that N、 丌=RTCy=RT this means that the differential equation for the time evolution of the volume of either compartment is NOT going to be linear!(since the right hand side will have 1/V terms.) This means that v(t) is NOT an exponential! However, we do know that it does asymptote to a final value and from numerical solvers we know it will look kind of like this 2V Vn/ Look in text or lecture notes for better version of the graph More measurements on cells How can we measure osmosis? Measure cell volume at equilibrium when you stick the cell in different bath osmolarities. But wait! Isn't that going to be horribly non-linear? Yes, but if you plot it right it's pretty easy to interpretReally the most useful equations (the ones you really want to understand). With these you can solve almost all the problems we will throw at you about osmosis. Things to remember though: 1. Be careful with the signs! Draw a diagram with which direction you are defining flux and be consistent. (the equations written here are only if you define the flux the way I’ve drawn it) 2. Check you unit! (always very helpful…) 3. Before starting the mathy part of the problem, stop and think about what will happen. Will the volume increase or decrease? At equilibrium, what will the concentrations of solutes have to be? 4. Once you finish all the math, check again to make sure that your answer makes sense… Time behavior of volume in osmosis problem: Plugging in from the equations above: F = - 1 d (V1(t)) = Lv (( p1 -p1) - ( p2 -p 2 )) A dt but you also know that: p = RTCS = RT � � � Ł V N ( S t) � ł � � this means that the differential equation for the time evolution of the volume of either compartment is NOT going to be linear! (since the right hand side will have 1/V terms…) This means that V(t) is NOT an exponential! However, we do know that it does asymptote to a final value and from numerical solvers we know it will look kind of like this: 2Vn Vn Vn/2 time Look in text or lecture notes for better version of the graph… More measurements on cells! How can we measure osmosis? Measure cell volume at equilibrium when you stick the cell in different bath osmolarities. But wait! Isn’t that going to be horribly non-linear? Yes, but if you plot it right it’s pretty easy to interpret… v