QuestionJuly 22, 2025

Use the References to access important values if needed for this question. The osmolarity of physiological saline solution is 0.300osmol/L. Assuming a membrane that is permeable only to water, what % (w/v) chromium (III) nitrate, Cr(NO_(3))_(3) solution is isotonic to physiological saline? square % (w/v)

Use the References to access important values if needed for this question. The osmolarity of physiological saline solution is 0.300osmol/L. Assuming a membrane that is permeable only to water, what % (w/v) chromium (III) nitrate, Cr(NO_(3))_(3) solution is isotonic to physiological saline? square % (w/v)
Use the References to access important values if needed for this question. The osmolarity of physiological saline solution is 0.300osmol/L. Assuming a membrane that is permeable only to water, what % (w/v) chromium (III) nitrate, Cr(NO_(3))_(3) solution is isotonic to physiological saline? square % (w/v)

Solution
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Answer

1.79\% \, (w/v) Explanation 1. Calculate Molarity of Chromium (III) Nitrate The osmolarity of the solution is 0.300 \, \text{osmol/L}. Since chromium (III) nitrate dissociates into 4 ions (Cr^{3+} and 3NO_3^-), the molarity needed for isotonicity is \frac{0.300}{4} = 0.075 \, \text{mol/L}. 2. Calculate Mass of Chromium (III) Nitrate per Liter Molar mass of Cr(NO_3)_3 is 238.01 \, \text{g/mol}. Therefore, mass per liter is 0.075 \, \text{mol/L} \times 238.01 \, \text{g/mol} = 17.85075 \, \text{g/L}. 3. Convert to \% (w/v) \% (w/v) is calculated as \left(\frac{\text{mass of solute in g}}{\text{volume of solution in mL}}\right) \times 100. Thus, \frac{17.85075 \, \text{g}}{1000 \, \text{mL}} \times 100 = 1.785075\%.

Explanation

1. Calculate Molarity of Chromium (III) Nitrate<br /> The osmolarity of the solution is $0.300 \, \text{osmol/L}$. Since chromium (III) nitrate dissociates into 4 ions ($Cr^{3+}$ and $3NO_3^-$), the molarity needed for isotonicity is $\frac{0.300}{4} = 0.075 \, \text{mol/L}$.<br /><br />2. Calculate Mass of Chromium (III) Nitrate per Liter<br /> Molar mass of $Cr(NO_3)_3$ is $238.01 \, \text{g/mol}$. Therefore, mass per liter is $0.075 \, \text{mol/L} \times 238.01 \, \text{g/mol} = 17.85075 \, \text{g/L}$.<br /><br />3. Convert to $\% (w/v)$<br /> $\% (w/v)$ is calculated as $\left(\frac{\text{mass of solute in g}}{\text{volume of solution in mL}}\right) \times 100$. Thus, $\frac{17.85075 \, \text{g}}{1000 \, \text{mL}} \times 100 = 1.785075\%$.
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