The osmotic pressure of blood is 7.85 atm at `25^(@) 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 solve the problem of determining the number of moles of glucose required for an intravenous injection that matches the osmotic pressure of blood, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Osmotic Pressure**:
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = CRT \]
where:
- \( \pi \) = osmotic pressure
- \( C \) = concentration (in moles per liter)
- \( R \) = universal gas constant
- \( T \) = temperature (in Kelvin)

2. **Convert Temperature to Kelvin**:
The temperature is given as \( 25^\circ C \). To convert this to Kelvin:
\[ T = 25 + 273 = 298 \, K \]

3. **Identify Given Values**:
From the problem, we have:
- Osmotic pressure \( \pi = 7.85 \, atm \)
- Volume \( V = 1 \, L \) (since we are calculating per liter)
- Gas constant \( R = 0.0821 \, atm \, L \, K^{-1} \, mol^{-1} \)

4. **Rearrange the Formula to Find Concentration**:
We can rearrange the osmotic pressure formula to solve for concentration \( C \):
\[ C = \frac{\pi}{RT} \]

5. **Substitute the Values into the Formula**:
Now, substitute the known values into the rearranged formula:
\[ C = \frac{7.85 \, atm}{(0.0821 \, atm \, L \, K^{-1} \, mol^{-1})(298 \, K)} \]

6. **Calculate the Concentration**:
Performing the calculation:
\[ C = \frac{7.85}{(0.0821)(298)} \approx \frac{7.85}{24.4758} \approx 0.32 \, mol/L \]

7. **Conclusion**:
Therefore, the number of moles of glucose required per liter for the intravenous injection is approximately:
\[ \text{Number of moles of glucose} \approx 0.32 \, mol \]