Question

The osmotic pressure of blood is 7.65 atm at 310 K. An aqueous solution of glucose isotonic with blood has the percentage (by volume)

• A. 5.41%
• B. 3.54%
• C. 4.53%
• D. 53.4%

Answer 1

Answer: (A)

5.41%

Answer 2

For an isotonic solution, the osmotic pressure $\pi$ is given by

$$\pi = iMRT$$

For glucose, $i=1$. Thus,

$$M = \frac{\pi}{RT}$$

Substitute the values:

$$M = \frac{7.65\, \text{atm}}{0.0821\, \text{L·atm/(mol·K)} \times 310\, \text{K}} \approx \frac{7.65}{25.451} \approx 0.300\, \text{M}$$

Now, calculate the mass of glucose in 1 L. The molar mass of glucose ($C_6H_{12}O_6$) is approximately 180 g/mol.

$$\text{Mass of glucose} = 0.300\, \text{mol/L} \times 180\, \text{g/mol} \approx 54\, \text{g/L}$$

Since percentage concentration (by weight/volume) is defined as

$$\%\ \text{(w/v)} = \frac{\text{g of solute in 100 mL solution}}{100\, \text{mL}} \times 100\%$$

we have

$$\text{Percentage} = \frac{54\, \text{g}}{1000\, \text{mL}} \times 100 = 5.4\%$$

Thus, the isotonic glucose solution is approximately 5.41%.