At `37^@C` , the osmotic pressure of blood is 8.21 atm . The amount of glucose that should be used per litre for an intravenous injection so that it becomes isotonic with blood is

Options

A. 117 g
B. 58.06 g
C. 108 g
D. 580.6 g

Answer

To solve the problem, we need to determine the amount of glucose required to create a solution with the same osmotic pressure as blood at 37°C, which is 8.21 atm.

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (π) of a solution can be calculated using the formula:
\[ \pi = iCRT \]
where:
- \( \pi \) = osmotic pressure (in atm)
- \( i \) = van 't Hoff factor (for glucose, \( i = 1 \) since it does not dissociate)
- \( C \) = molarity of the solution (in mol/L)
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin (K)

### Step 2: Convert the temperature to Kelvin
The temperature in Celsius can be converted to Kelvin using the formula:
\[ T(K) = T(°C) + 273.15 \]
For 37°C:
\[ T = 37 + 273.15 = 310.15 \, K \]

### Step 3: Rearrange the osmotic pressure formula to find molarity (C)
Since we know the osmotic pressure (π = 8.21 atm), we can rearrange the formula to solve for molarity (C):
\[ C = \frac{\pi}{iRT} \]
Substituting the values:
- \( \pi = 8.21 \, \text{atm} \)
- \( i = 1 \)
- \( R = 0.0821 \, \text{L·atm/(K·mol)} \)
- \( T = 310.15 \, K \)

### Step 4: Calculate the molarity (C)
\[ C = \frac{8.21}{1 \times 0.0821 \times 310.15} \]
Calculating the denominator:
\[ C = \frac{8.21}{0.0821 \times 310.15} = \frac{8.21}{25.485215} \approx 0.322 \, \text{mol/L} \]

### Step 5: Calculate the mass of glucose required
Now, we need to find the mass of glucose required to achieve this molarity. The molar mass of glucose (C6H12O6) is approximately 180.18 g/mol. The mass (m) can be calculated using:
\[ m = C \times \text{molar mass} \times \text{volume} \]
Assuming we want to prepare 1 liter of solution:
\[ m = 0.322 \, \text{mol/L} \times 180.18 \, \text{g/mol} \times 1 \, \text{L} \]
Calculating the mass:
\[ m \approx 0.322 \times 180.18 \approx 58.1 \, \text{g} \]

### Final Answer
The amount of glucose that should be used per liter for an intravenous injection to make it isotonic with blood is approximately **58.1 grams**.

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