How to Calculate Solute Potential

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Osmosis is a vital process for living organisms. It's the phenomenon whereby water migrates across a semi-permeable barrier from the side with the least concentration of solutes to the side with the most concentration. The force driving this process is osmotic pressure, and it depends on the concentration of solute on both sides of the barrier. The bigger the difference, the stronger the osmotic pressure. This difference is called solute potential, and it depends on temperature and the number of particles of solute, which you can calculate from the molar concentration and a quantity called the ionization constant.

TL;DR (Too Long; Didn't Read)

The solute potential (ψs) is the product of the ionization constant (i) of the solute, its molar concentration (C), the temperature in Kelvins (T) and a constant called the pressure constant (R). In mathematical form:

ψs = iCRT

Ionization Constant

When a solute dissolves in water, it breaks into its component ions, but it may not do so completely, depending on its composition. The ionization constant, also called the dissociation constant, is the sum of ions to unionized molecules of solute. In other words, it's the number of particles the solute will make in water. Salts that dissolve completely have an ionization constant of 2. Molecules that remain intact in water, such as sucrose and glucose, have an ionization constant of 1.

Molar Concentration

You determine the concentration of particles by calculating molar concentration, or molarity. You arrive at this quantity, which is expressed in moles per liter, by calculating the number of moles of solute and dividing by the volume of solution.

To find the number of moles of solute, divide the weight of the solute by the molecular weight of the compound. For example, sodium chloride has a molecular weight of 58 g/mol, so if you have a sample weighing 125 g, you have 125 g ÷ 58 g/mole = 2.16 moles. Now divide the number of moles of solute by the volume of solution to find the molar concentration. If you dissolve 2.16 moles of sodium chloride in 2 liters of water, you have a molar concentration of 2.16 moles ÷ 2 liters = 1.08 moles per liter. You can also express this as 1.08 M, where "M" stands for "molar."

Formula for Solute Potential

Once you know the ionization potential (i) and the molar concentration (C), you know how many particles the solution contains. You relate this to osmotic pressure by multiplying by the pressure constant (R), which is 0.0831 liter bar/mole oK. Since the pressure is dependent on temperature, you must also factor this into the equation by multiplying by the temperature in degrees Kelvin, which is equal to the temperature in degrees Celsius plus 273. The formula for solute potential (ψs) is:

ψs = iCRT

Example

Calculate the solute potential of a 0.25 M solution of calcium chloride at 20 degrees Celsius.

Calcium chloride completely dissociates into calcium and chlorine ions, so its ionization constant is 2, and the temperature in degrees Kevin is (20 + 273) = 293 K. The solute potential is therefore (2 • 0.25 moles/liter • 0.0831 liter bar/mole K • 293 K)

= 12.17 bars.

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