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

Options

A. `5.41`
B. `3.54`
C. `4.53`
D. `53.4`

Explanation

To find the percentage (wt/volume) of an aqueous glucose solution that is isotonic with blood, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Osmotic Pressure**:
- Osmotic pressure (π) is the pressure required to stop the flow of solvent through a semipermeable membrane. For a solution to be isotonic with blood, its osmotic pressure must equal that of blood.

2. **Given Data**:
- Osmotic pressure of blood (π) = 7.65 atm
- Temperature (T) = 310 K
- Molecular weight of glucose (C6H12O6) = 180 g/mol

3. **Use the Formula for Osmotic Pressure**:
- The formula for osmotic pressure is given by:
\[ \pi = CRT \]
where:
- \(C\) = concentration in moles per liter (mol/L)
- \(R\) = universal gas constant = 0.0821 L·atm/(K·mol)
- \(T\) = temperature in Kelvin

4. **Rearranging the Formula**:
- We can rearrange the formula to find the concentration \(C\):
\[ C = \frac{\pi}{RT} \]

5. **Substituting the Values**:
- Substitute the known values into the equation:
\[ C = \frac{7.65 \, \text{atm}}{0.0821 \, \text{L·atm/(K·mol)} \times 310 \, \text{K}} \]

6. **Calculating the Concentration**:
- Calculate the denominator:
\[ 0.0821 \times 310 = 25.451 \]
- Now calculate \(C\):
\[ C = \frac{7.65}{25.451} \approx 0.301 \, \text{mol/L} \]

7. **Convert Molarity to Grams per Liter**:
- To find the mass of glucose in grams per liter, use the molecular weight:
\[ \text{mass (g/L)} = C \times \text{molecular weight} = 0.301 \, \text{mol/L} \times 180 \, \text{g/mol} \]
- Calculate:
\[ \text{mass} \approx 54.18 \, \text{g/L} \]

8. **Convert Grams per Liter to Percentage (wt/volume)**:
- The percentage (wt/volume) is calculated as:
\[ \text{Percentage} = \left(\frac{\text{mass (g)}}{\text{volume (mL)}}\right) \times 100 \]
- For 1 L (1000 mL):
\[ \text{Percentage} = \left(\frac{54.18 \, \text{g}}{1000 \, \text{mL}}\right) \times 100 \approx 5.418\% \]

9. **Final Result**:
- The percentage of glucose solution that is isotonic with blood is approximately **5.41%**.