To calculate the osmolarity of a 50% (w/v) MgSO₄ solution, follow these steps:

Step 1: Understand the Definition of 50% (w/v)

• A 50% (w/v) solution means 50 grams of solute (MgSO₄) per 100 mL of solution.
• So, we have 50 grams of MgSO₄ in 100 mL of solution.

Step 2: Calculate the Molarity (mol/L)

We need to find how many moles of MgSO₄ are in 1 liter (1000 mL) of solution. First, convert 50 grams of MgSO₄ in 100 mL to grams per liter: $\frac{50 \text{ g}}{100 \text{ mL}} \times 1000 \text{ mL/L} = 500 \text{ g/L}$ Next, use the molecular weight (MW) of MgSO₄ (120.4 g/mol) to find the molarity: $\text{Molarity} = \frac{500 \text{ g/L}}{120.4 \text{ g/mol}} \approx 4.15 \text{ mol/L}$

Step 3: Calculate the Osmolarity (mOsmol/L)

MgSO₄ dissociates into two particles in solution: $\text{Mg}^{2+}$ and $\text{SO}_4^{2-}$. Thus, for every 1 mole of MgSO₄, there are 2 osmoles of particles. Therefore, osmolarity is: $\text{Osmolarity} = 4.15 \text{ mol/L} \times 2 = 8.30 \text{ Osmol/L} = 8300 \text{ mOsmol/L}$

Final Answer:

The osmolarity of the 50% (w/v) MgSO₄ solution is 8300 mOsmol/L, rounded to the nearest whole number.

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Do you want more details or have any questions about this?
Here are 5 questions to expand your understanding:

1. How does dissociation affect the osmolarity of a solution?
2. Why is osmolarity important in medical and biological contexts?
3. How would the osmolarity change if MgSO₄ only partially dissociated?
4. What is the difference between molarity and osmolarity?
5. How do different solutes affect the tonicity of a solution?

Tip: When calculating osmolarity, always account for how many particles a solute dissociates into in solution!