The osmotic pressure of blood is 8.21 atm at `27^(@) C`.The number of mol of glucose to be used per litre for an intravenous injection that is to have the same osmotic pressure as blood is

Answer

To find the number of moles of glucose needed to achieve the same osmotic pressure as blood, we can use the formula for osmotic pressure:

\[ \pi = C \cdot R \cdot T \]

Where:
- \(\pi\) is the osmotic pressure,
- \(C\) is the concentration in moles per liter,
- \(R\) is the gas constant,
- \(T\) is the temperature in Kelvin.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Osmotic pressure (\(\pi\)) = 8.21 atm
- Temperature = 27°C

2. **Convert Temperature to Kelvin:**
\[ T(K) = 27 + 273 = 300 \, K \]

3. **Use the Gas Constant:**
- The value of \(R\) (gas constant) is 0.0821 atm·L/(K·mol).

4. **Rearrange the Osmotic Pressure Formula to Solve for Concentration (C):**
\[ C = \frac{\pi}{R \cdot T} \]

5. **Substitute the Known Values into the Equation:**
\[ C = \frac{8.21 \, \text{atm}}{0.0821 \, \text{atm·L/(K·mol)} \cdot 300 \, K} \]

6. **Calculate the Concentration (C):**
\[ C = \frac{8.21}{0.0821 \cdot 300} = \frac{8.21}{24.63} \approx 0.333 \, \text{mol/L} \]

7. **Determine the Number of Moles of Glucose Needed per Liter:**
Since the concentration \(C\) is in moles per liter, the number of moles of glucose needed for an intravenous injection to match the osmotic pressure of blood is approximately:
\[ \text{Number of moles} \approx 0.33 \, \text{mol} \]

### Final Answer:
The number of moles of glucose to be used per liter for an intravenous injection that is to have the same osmotic pressure as blood is approximately **0.33 moles**.