Question

For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) Human blood gives rise to an osmotic pressure of approximately \(7.65\) atm at body temperature, \(37^\circ\text{C}\). Hence, molarity of an intravenous glucose solution to have the same osmotic pressure as blood is _____ M

Hint:

For non-electrolytes like glucose, van’t Hoff factor \( i = 1 \), so use \( \pi = MRT \).

Answer 1

Correct Answer: 0.3

Step 1: Osmotic pressure is given by the relation \[ \pi = MRT \] where \( \pi \) is osmotic pressure, \( M \) is molarity, \( R \) is gas constant, and \( T \) is absolute temperature.
Step 2: Given: \[ \pi = 7.65\,\text{atm}, \quad T = 37^\circ\text{C} = 310\,\text{K}, \] \[ R = 0.0821\,\text{L atm mol}^{-1}\text{K}^{-1}. \]
Step 3: Rearranging the formula, \[ M = \frac{\pi}{RT}. \]
Step 4: Substituting values, \[ M = \frac{7.65}{0.0821 \times 310} = \frac{7.65}{25.45} \approx 0.30. \] Hence, the required molarity is \[ \boxed{0.30\,\text{M}}. \]