The osmotic pressure of blood is 7.65 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. `0.3`
B. `0.2`
C. `0.1`
D. `0.4`

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:

\[ \pi = \frac{n}{V}RT \]

Where:
- \(\pi\) = osmotic pressure (in atm)
- \(n\) = number of moles of solute (glucose in this case)
- \(V\) = volume of solution (in liters)
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature (in Kelvin)

### Step 1: Convert temperature to Kelvin
Given temperature is \(27^\circ C\):
\[ T = 27 + 273 = 300 \, K \]

### Step 2: Identify the osmotic pressure
The osmotic pressure of blood is given as:
\[ \pi = 7.65 \, atm \]

### Step 3: Set the volume of the solution
For intravenous injection, we assume the volume \(V\) is 1 liter:
\[ V = 1 \, L \]

### Step 4: Use the osmotic pressure formula to find \(n\)
Rearranging the formula for \(n\):
\[ n = \frac{\pi V}{RT} \]

### Step 5: Substitute the known values into the equation
Substituting the values we have:
\[ n = \frac{7.65 \, atm \times 1 \, L}{0.0821 \, L·atm/(K·mol) \times 300 \, K} \]

### Step 6: Calculate \(n\)
Calculating the denominator:
\[ 0.0821 \, L·atm/(K·mol) \times 300 \, K = 24.63 \, L·atm/mol \]

Now substituting back into the equation for \(n\):
\[ n = \frac{7.65}{24.63} \approx 0.310 \, mol \]

### Step 7: Round the answer
Rounding to two decimal places, we find:
\[ n \approx 0.31 \, mol \]

### 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 **0.31 moles**.

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