AP Bio Math Fun - Osmosis

Ace AP Bio osmosis math! Master calculations for water potential & solute potential. Understand water movement.

Osmosis Math There are three main equations you need to be prepared to use for osmosis: percent change, water potential, and solute potential.Let's start with percent change. Determining a percent allows for direct comparison across different sizes or types of materials. In order to do this you simply plug into the following formula:[(final mass - initial mass) / initial mass] *100Try the following problems :) A piece of zucchini had an initial mass of 20g and a final mass of 10g. What is the percent change in mass? -50% 50% -100% 100% A piece of lettuce had an initial mass of 5g and a final mass of 10g. What is the percent change in mass? -50% 50% -100% 100% A dialysis bag had an initial mass of 7.4g and a final mass of 8.2g. What is the percent change in mass? -10.8% 10.8% -9.75% 9.75% What does it mean if your answer is negative? That you've done something wrong That the object lost mass That the object gained mass Water Potential and Solute Potential When you're determining the water potential (a lot of water has a high water potential, less water has a lower potential) it's important to understand a few key facts.1. If there is MORE solute in the solution then it is hypertonic2. If there is LESS solute then it is hypotonic1. The hypertonic solution has a lower water potential since there's physically less space for the water.2. The hypotonic solution has higher water potential since there's physically more space for the water.Water moves from its high water potential to its low water potential. This is just diffusion.So water moves from the hypotonic solution to the hypertonic solution.Solute potential is one of the key factors in determining the overall water potential. (duh... as the solute gets higher the water potential gets lower.) Water Potential and Pressure Potential Besides the solute potential water potential can be impacted by pressure.If you apply pressure to the solution the water tends to move out of the area... imagine squeezing a bottle of water hard... the water leaves due to pressure. Water Potential Equation When you calculate the water potential you have to take into account both the solute potential and the pressure potential. This can be done mathematically using the following formula:ψ = ψs + ψpwhere ψ is the water potential, ψs is the solute potential, and ψp is the pressure potential. Calculating Solute Potential If a solution has NO solute (distilled water) it has an obvious solute potential of 0.Any addition of solute becomes a negative number. The negative indicates lessspace for water.In an open container, where there's no pressure, the water potential will simply equal the solute potentialψ = ψs + ψpψ = ψs + 0ψ = ψsCheck out the following caseψ = ψs + ψpOpen container so...ψ = ψs + 0ψ = -9This indicates (because of the negative... aka lower... water potential) that water would "want" to move into this solution from any solution that is more positive than -9.Let's try some out! Container A is an open container that has a solute potential of -2. What is the water potential? -2 2 what? Container B is a container of distilled water with a pressure potential of +4. What is the water potential? +4 -4 what? Container C is has a ψs=-7 and ψp of 3. What is the water potential? -4 -10 4 10 what? Since water travels from its high water potential to its low water potential which container (A,B, or C) would water most want to travel INTO. A B C what? Calculating ψs So now we know what to do if we're given ψs and ψp and also what to do to find out if ψs or ψp is zero. What if they don't give us ψs... is there a way to figure it out?YES!ψs can be easily calculated if you know the molarity of the solution you're working with. That molarity can be determined on a graph where the change in mass crosses the 0 line (indicating no gain or loss of mass=isotonic). This is what our lab did.We can use the formulaψs = -iCRT- because we always have a negative to indicate the addition of solutesi is the ionization constant (how many ions your solute breaks into) They'll tell you this OR they'll use sucrose which has an i or 1 since it doesn't ionize in water.C is the molar concentration (you get that from your graph or they tell you)R is a constant... it's always 0.0831 liter bar °KT is temperature in K so take your celsius temp and add 273.Let's give it a try! A dialysis bag with an unknown sucrose solution is placed in several solutions to determine percent mass change. After graphing the line shows a molarity of 0.25M. The temperature of the room is 22°C. What is the ψs? -6.13 6.13 what? That same bag has no pressure on it (Meg is NOT squeezing it). What is the ψ of the fluid in the bag? -6.13 6.13 what? This bag is placed in an open container of solution that measures .2 molarity of sucrose. What is the ψ of the solution? 4.9 -4.9 what? Will water move into or out of the bag? into the bag out of the bag Where does the water go? So there are two ways to determine where the water will travel.1. we can look at the molarities of the solutions... water will travel to the higher molarity=hypertonic=lowψ2. we can calculate the ψ knowing that water goes to the lower potential. Calculate Water Potential and Predict Movement On the image below complete each of the following1. determine ψ of the beaker2. determine ψ of the dialysis bag3. determine the direction of water movement