The osmotic pressure of blood is 6.75 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

Options

A. 0.27
B. 0.15
C. 0.57
D. 0.67

Explanation

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

\[ \pi = CRT \]

Where:
- \(\pi\) = osmotic pressure (in atm)
- \(C\) = concentration (in moles per liter)
- \(R\) = universal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature (in Kelvin)

### Step-by-Step Solution:

1. **Identify Given Values:**
- Osmotic pressure (\(\pi\)) = 6.75 atm
- Temperature = 27°C

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

3. **Use the Osmotic Pressure Formula:**
Rearranging the formula to find concentration \(C\):
\[ C = \frac{\pi}{RT} \]

4. **Substitute the Known Values:**
- \(\pi = 6.75 \, \text{atm}\)
- \(R = 0.0821 \, \text{L·atm/(K·mol)}\)
- \(T = 300 \, K\)

Substituting these values into the equation:
\[ C = \frac{6.75}{0.0821 \times 300} \]

5. **Calculate the Denominator:**
\[ 0.0821 \times 300 = 24.63 \]

6. **Calculate the Concentration \(C\):**
\[ C = \frac{6.75}{24.63} \approx 0.273 \, \text{mol/L} \]

7. **Conclusion:**
The number of moles of glucose needed per liter for the intravenous injection is approximately **0.273 moles**.

### 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 **0.273 moles**.