Osmolarity, the number of moles of osmotically active species (osmoles) per liter of solution (Osmol/L), equals the molar solute concentration M multiplied by the van 't Hoff factor i. Osmolarity is calculated by dividing osmotic pressure Π by RT, where R is the gas constant and T is the absolute temperature.If the osmotic pressure of blood plasma is 6.9 atm at 37 °C, what is its osmolarity? (Note: Assume R = 0.08 L·atm/mol·K, and i = 2.)

Question

Osmolarity, the number of moles of osmotically active species (osmoles) per liter of solution (Osmol/L), equals the molar solute concentration M multiplied by the van 't Hoff factor i.  Osmolarity is calculated by dividing osmotic pressure Π by RT, where R is the gas constant and T is the absolute temperature.If the osmotic pressure of blood plasma is 6.9 atm at 37 °C, what is its osmolarity?  (Note:  Assume R = 0.08 L·atm/mol·K, and i = 2.)

Quizplus · Accepted Answer

11ecba2d_11f4_7216_a3bf_c9e975e189bb_MD0008_00 The diffusion of solvent across a semipermeable membrane from a solution of lower concentration to a solution of higher concentration during osmosis produces an osmotic pressure against the membrane. Dissolved ions or molecules that cannot cross the membrane are osmotically active because they cause a concentration difference that induces the solvent diffusion. Accordingly, the osmotic pressure is proportional to the molar concentration of osmotically active solute species (the osmolarity), which is calculated by i·M. The concentration (molarity, M) of the bulk solute is not necessarily equivalent to the osmolarity because some solutes can dissociate into ions. For example, NaCl dissociates into two ions (Na⁺ and Cl⁻), which causes its osmolarity to be twice the NaCl concentration. To account for this, the van 't Hoff factor i is used, which is a coefficient related to the number of moles of osmotically active ions or molecules (osmoles) that a solute molecule will form when dissolved. In complex solutions with mixtures of different solutes, determining i can become complicated. Consequently, i may be estimated or the measured osmolarity may be evaluated directly instead. If the osmotic pressure of blood plasma is 6.9 atm at physiological temperature (37 °C), the osmolarity of the plasma can be calculated as: 11ecba2d_11f4_7217_a3bf_df47069e4297_MD0008_00 (Choice A) Solving for molarity (M) instead of osmolarity (i·M) results in a value of 0.14 mol/L, which is the concentration of the nondissociated solutes rather than the concentration of all osmotically active species. (Choice C) If the temperature is not converted from Celsius to Kelvin and the equation is also solved for molarity (M) instead of osmolarity (i·M), a value of 1.2 mol·K/°C·L is obtained (incorrect units). (Choice D) Using the temperature in Celsius instead of Kelvin gives a value of 2.3 mol·K/°C·L (incorrect units). Educational objective: Solvent diffusion across the semipermeable membrane during osmosis produces an osmotic pressure against the membrane proportional to the osmolarity (concentration of osmotically active species that cannot cross the membrane) rather than to the solute molarity due to the dissociation of some solutes. Solute concentration and osmolarity are related by the van 't Hoff factor.

Osmolarity, the Number of Moles of Osmotically Active Species (Osmoles)