The osmotic pressure of blood is 8.65 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 needed for an intravenous injection that matches the osmotic pressure of blood, we can use the formula for osmotic pressure:

\[ \pi = CRT \]

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

### Step-by-Step Solution:

**Step 1: Identify the given values.**
- Osmotic pressure (\(\pi\)) = 8.65 atm
- Temperature = 25°C

**Hint:** Remember to convert the temperature from Celsius to Kelvin.

**Step 2: Convert the temperature to Kelvin.**
\[ T = 25 + 273 = 298 \, K \]

**Hint:** Use the formula \(T(K) = T(°C) + 273\) for conversion.

**Step 3: Rearrange the osmotic pressure formula to solve for concentration \(C\).**
\[ C = \frac{\pi}{RT} \]

**Hint:** Isolate \(C\) by dividing both sides of the equation by \(RT\).

**Step 4: Substitute the known values into the equation.**
\[ C = \frac{8.65 \, \text{atm}}{0.0821 \, \text{atm·L/(mol·K)} \times 298 \, K} \]

**Hint:** Make sure to keep the units consistent when substituting values.

**Step 5: Calculate the concentration \(C\).**
\[ C = \frac{8.65}{0.0821 \times 298} \approx \frac{8.65}{24.4758} \approx 0.353 \, \text{mol/L} \]

**Hint:** Perform the multiplication in the denominator first before dividing.

**Step 6: Conclusion.**
The number of moles of glucose needed per liter for the intravenous injection is approximately 0.35 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 **0.35 moles**.