Question

Osmosis occurs when two solutions of different concentrations are separated by a semipermeable membrane. The membrane allows solvent particles, but not solute particles, to pass through. Thus, the solvent moves toward the solution of higher concentration (to dilute it) until the two solutions have the same concentration, or until gravity overtakes the osmotic pressure, Π. The osmotic pressure between a solution and pure solvent depends on the number of solute particles and thus is a colligative property. It can be expressed asΠ=MRTwhere M is the total molarity of the solute particles, R=0.08206L⋅atm/(K⋅mol) is the gas constant, and T is the Kelvin temperature.Part AIsotonic saline solution, which has the same osomotic pressure as blood, can be prepared by dissolving 0.923 g of NaCl in enough water to produce 100. mL of solution. What is the osmotic pressure of this solution at 25 ∘C?Part BWhen the isotonic saline solution described in part A is connected to an unknown solution via a semipermeable membrane, the unknown solution level drops. Based on this information, what can be said about these two solutions?The two solutions have the same concentration.The unknown solution had the lower concentration.The unknown solution had the higher concentration.Part COsmosis is the process responsible for carrying nutrients and water from groundwater supplies to the upper parts of trees. The osmotic pressures required for this process can be as high as 20.1 atm . What would the molar concentration of the tree sap have to be to achieve this pressure on a day when the temperature is 21 ∘C ?

Answer 1

Part A → 7.82 atm

Part B → The unknown solution had the higher concentration

Part C → 0.83 mol/L

Step-by-step explanation:

Part A

Osmotic pressure (π) = M . R. T . i

NaCl → Na⁺ + Cl⁻ (i =2)

0.923 g of NaCl must be dissolved in 100 mL of solution.

0.923 g / 58.45 g/m = 0.016 moles

Molarity is mol/L → 0.016 m / 0.1L = 0.16M

π = 0.16M . 0.08206 L.atm/molK . 298K . 2 ⇒ 7.82atm

Part. B

The solvent moves toward the solution of higher concentration (to dilute it) until the two solutions have the same concentration, or until gravity overtakes the osmotic pressure, Π. If the level of the unknown solution drops when it was connected to solution in part A, we can be sure that had a higher concentration.

Part. C

π = M . R . T

20.1 atm = M . 0.08206 L.atm/mol.K . 294K

20.1 atm / (0.08206 L.atm/mol.K . 294K) = 0.83 mol/L