Question

What is the osmolarity of the following solutions? (a) \(0.35 M \mathrm{KBr}\) (b) \(0.15 M\) glucose \(+0.05 M \mathrm{~K}_{2} \mathrm{SO}_{4}\)

Short answer

(a) 0.70 osmoles/L; (b) 0.30 osmoles/L.

Step-by-step solution

Understanding Osmolarity

Osmolarity is the total concentration of all solute particles in a solution. It's calculated by adding the contribution of each solute's molarity multiplied by the number of particles it dissociates into.

Calculate for KBr

Potassium bromide (KBr) dissociates into two ions: K⁺ and Br⁻. Therefore, 1 mole of KBr will yield 2 moles of particles. The osmolarity for KBr is calculated as:\[0.35 \text{ M} \times 2 = 0.70 \text{ osmoles/L}\]

Calculate for Glucose

Glucose does not dissociate into ions in solution, so it remains as one particle. Therefore, the osmolarity contribution from glucose is the same as its molarity, which is 0.15 M.

Calculate for K2SO4

Potassium sulfate (K₂SO₄) dissociates into three ions: 2 K⁺ and 1 SO₄²⁻. Thus, 1 mole of K₂SO₄ yields 3 moles of particles. The osmolarity for K₂SO₄ is:\[0.05 \text{ M} \times 3 = 0.15 \text{ osmoles/L}\]

Calculate Total Osmolarity for Part (b)

Add the osmolarity contributions for glucose and K₂SO₄ together:\[0.15 \text{ osmoles/L (glucose)} + 0.15 \text{ osmoles/L (}\mathrm{K}_2\mathrm{SO}_4\text{)} = 0.30 \text{ osmoles/L}\]

Key concepts

Molarity

Molarity is a measure of the concentration of solute in a solution. It's defined as the number of moles of solute per liter of solution, abbreviated as "M". Understanding molarity helps in calculating how much of a substance is dissolved in a given volume of liquid.
For example, when we say a solution has a molarity of 0.35 M KBr, it means there are 0.35 moles of potassium bromide dissolved in every liter of solution. Molarity is a central concept in chemistry because it allows chemists to predict how a solution will behave in reactions, especially when it comes to mixing different solutions. Calculating molarity involves taking into account the total volume of the solution, which is vital for accurate measurements in laboratory settings.
To find the molarity, the formula is as follows:

• Molarity (M) = Moles of solute / Liters of solution

This simple ratio helps us understand how concentrated a given solution is.

Dissociation

Dissociation refers to the process by which molecules split into smaller particles, such as ions, when dissolved in a solvent like water. It's a critical concept that explains how substances like salts and acids behave when they are mixed with water.
In the example exercise, KBr dissociates in water into K⁺ and Br⁻ ions. This means that when one mole of KBr dissolves, it produces 2 moles of ions in total. Understanding dissociation is essential for calculating osmolarity, as the number of particles each solute produces will influence the solution's properties.
Glucose, however, does not dissociate like ionic compounds. It remains as individual glucose molecules when dissolved, so its molarity and osmolarity are the same.

Ions

Ions are charged particles formed by the loss or gain of electrons. In solutions, ions interact with the solvent, which affects the solution's overall properties. They are the building blocks for understanding processes like conductivity and osmotic pressure.
When compounds like salts dissolve in water, they often dissociate into ions, which can carry an electric charge. For example, in our problem, KBr dissociates into K⁺ and Br⁻ ions. The presence of these ions in solution is what defines the ionic strength of the solution.
Ions are pivotal in calculating the osmolarity of a solution because each dissociated ion contributes individually to the total number of particles in the solution. As a rule of thumb, the more ions present, the higher the osmolarity of the solution.

Solution Concentration

Solution concentration quantifies the amount of solute present in a given quantity of solvent. It determines how strong or dilute a solution is, affecting how the solution will react chemically and physically.
In the context of our exercise, we considered how the concentration of each solute contributes to the total solution's osmolarity. By understanding the solutes' molarity and their dissociation behavior, we calculated the individual and total contributions to the solution concentration.

• For KBr: Contribution is based on its molarity and dissociation into 2 ions.
• For glucose: Contribution is based on its molarity only, as it does not dissociate.
• For K₂SO₄: Contribution depends on it dissociating into 3 ions.

In summary, the concentration of solutions depends on both the amount of solute added and their subsequent behavior in the solution, which is why osmolarity can differ even for solutions with the same molarity.