The osmotic pressure of blood is `8.21 atm` at `310 K`. How much glucose should be used per L for an intravenous injection that is isotonic with blood?

Options

A. 116.12
B. 58.06
C. 29.03
D. 87.09

Explanation

To find out how much glucose should be used per liter for an intravenous injection that is isotonic with blood, we can use the formula for osmotic pressure. Here’s a step-by-step solution:

### Step 1: Understand the relationship between osmotic pressure and concentration.
The osmotic pressure (π) of a solution can be calculated using the formula:
\[ \pi = \frac{n}{V}RT \]
where:
- \( \pi \) = osmotic pressure
- \( n \) = number of moles of solute
- \( V \) = volume of solution in liters
- \( R \) = universal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin

### Step 2: Identify the given values.
From the question, we have:
- Osmotic pressure of blood, \( \pi = 8.21 \, \text{atm} \)
- Temperature, \( T = 310 \, \text{K} \)
- Volume, \( V = 1 \, \text{L} \)

### Step 3: Rearrange the formula to find the number of moles of glucose.
We need to find \( n \):
\[ n = \frac{\pi V}{RT} \]

### Step 4: Substitute the known values into the equation.
Substituting the values into the equation:
\[ n = \frac{8.21 \, \text{atm} \times 1 \, \text{L}}{0.0821 \, \text{L·atm/(K·mol)} \times 310 \, \text{K}} \]

### Step 5: Calculate the number of moles.
Calculating the denominator:
\[ 0.0821 \times 310 = 25.451 \]
Now substituting back:
\[ n = \frac{8.21}{25.451} \approx 0.323 \, \text{moles} \]

### Step 6: Calculate the mass of glucose needed.
The mass of glucose (w) can be calculated using the formula:
\[ w = n \times M \]
where \( M \) is the molar mass of glucose (C₆H₁₂O₆), which is approximately 180 g/mol.
\[ w = 0.323 \, \text{moles} \times 180 \, \text{g/mol} \approx 58.14 \, \text{grams} \]

### Step 7: Conclusion.
To make the glucose solution isotonic with blood, approximately **58.14 grams of glucose** should be used per liter.

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