QuestionWhat sodium chloride concentration is needed for an isotonic solution with blood at $7.70 \, \mathrm{atm}$ ? Use $\pi = MRT$ .

Studdy Solution

STEP 1

Assumptions1. The osmotic pressure of blood is $7.70 \, \mathrm{atm}$ . The temperature at which the osmotic pressure is measured is $25^{\circ} \, \mathrm{C}$ or $298.15 \, \mathrm{K}$
3. The ideal gas constant $R$ is $0.0821 \, \mathrm{ \cdot atm/K \cdot mol}$
4. The osmotic pressure $\pi$ is given by the formula $\pi = MRT$ , where $M$ is the molar concentration, $R$ is the ideal gas constant, and $$ is the temperature in Kelvin.

STEP 2

We need to find the molar concentration $M$ of sodium chloride in water that will produce an aqueous solution isotonic with blood. We can rearrange the formula for osmotic pressure to solve for $M$ .
$M = \frac{\pi}{RT}$

STEP 3

Now, plug in the given values for the osmotic pressure $\pi$ , the ideal gas constant $R$ , and the temperature $$ to calculate the molar concentration $M$.
$M = \frac{7.70 \, \mathrm{atm}}{0.0821 \, \mathrm{ \cdot atm/K \cdot mol} \times298.15 \, \mathrm{K}}$

STEP 4

Perform the division to calculate the molar concentration $M$ .
$M = \frac{7.70 \, \mathrm{atm}}{0.0821 \, \mathrm{ \cdot atm/K \cdot mol} \times298.15 \, \mathrm{K}} =0.318 \, \mathrm{mol/L}$ The concentration of sodium chloride in water needed to produce an aqueous solution isotonic with blood is $0.318 \, \mathrm{mol/L}$ .

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