What is the osmolarity of a solution of 0.9% NaCl in mosmol, molecular weight of NaCl = 58.5?
Understand the Problem
The question is asking for the calculation of the osmolarity of a 0.9% NaCl solution. This entails determining the number of osmoles per liter based on the given percentage concentration and molecular weight of NaCl.
Answer
The osmolarity of the solution is approximately $0.308 \text{ osmol/L}$.
Answer for screen readers
The osmolarity of a 0.9% NaCl solution is approximately $0.308 \text{ osmol/L}$.
Steps to Solve
- Understand the percentage concentration
A 0.9% NaCl solution means there are 0.9 grams of NaCl in 100 mL of solution.
- Convert the volume to liters
Since osmolarity is expressed in osmoles per liter, convert the volume from mL to L: $$ 100 \text{ mL} = 0.1 \text{ L} $$
- Calculate the number of moles of NaCl
Using the molecular weight of NaCl, which is 58.5 g/mol, calculate the number of moles in 0.9 g: $$ \text{Moles of NaCl} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} = \frac{0.9 \text{ g}}{58.5 \text{ g/mol}} \approx 0.0154 \text{ moles} $$
- Determine the number of osmoles
NaCl dissociates into two ions (Na+ and Cl-), effectively doubling the osmoles: $$ \text{Osmoles} = 2 \times \text{moles of NaCl} \approx 2 \times 0.0154 \approx 0.0308 \text{ osmoles} $$
- Calculate the osmolarity
Using the formula for osmolarity, divide the total osmoles by the volume in liters: $$ \text{Osmolarity (osmol/L)} = \frac{\text{osmoles}}{\text{volume (L)}} = \frac{0.0308 \text{ osmoles}}{0.1 \text{ L}} \approx 0.308 \text{ osmol/L} $$
The osmolarity of a 0.9% NaCl solution is approximately $0.308 \text{ osmol/L}$.
More Information
Osmolarity is a crucial parameter in medicine and biology, indicating how many osmoles of solute are present in a solution. For NaCl, each molecule dissociates into two ions, making salt solutions particularly impactful in physiological contexts.
Tips
- Not accounting for dissociation: Failing to remember that NaCl dissociates into two ions can lead to incorrect osmolarity calculations.
- Unit conversion errors: Confusing mL and L or miscalculating the weight can distort the results.
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