The osmotic pressure of blood is 8.56 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 for an intravenous injection that has 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)
- \(R\) = gas constant (0.0821 atm·L/(K·mol))
- \(T\) = temperature (in Kelvin)

### Step-by-step Solution:

**Step 1: Convert the temperature from Celsius to Kelvin.**
\[ T(K) = T(°C) + 273 \]
Given \(T = 27°C\):
\[ T = 27 + 273 = 300 K \]

**Step 2: Rearrange the osmotic pressure formula to solve for concentration \(C\).**
\[ C = \frac{\pi}{RT} \]

**Step 3: Substitute the known values into the equation.**
We know:
- \(\pi = 8.56 \, \text{atm}\)
- \(R = 0.0821 \, \text{atm·L/(K·mol)}\)
- \(T = 300 \, K\)

Substituting these values:
\[ C = \frac{8.56}{0.0821 \times 300} \]

**Step 4: Calculate the concentration \(C\).**
First, calculate the denominator:
\[ 0.0821 \times 300 = 24.63 \]
Now substitute back into the equation:
\[ C = \frac{8.56}{24.63} \approx 0.347 \, \text{mol/L} \]

**Step 5: Conclusion.**
The number of moles of glucose needed per liter for the intravenous injection is approximately:
\[ \text{Number of moles} \approx 0.347 \, \text{mol} \]

### Summary:
To achieve the same osmotic pressure as blood, approximately **0.347 moles** of glucose should be used per liter.

---