Human blood gives rise to an osmotic pressure of approxi-mately 7.7 atm at body temperature, 37.0 °C. What must the molarity of an intravenous glucose solution be to give rise to the same osmotic pressure as blood?

Verified step by step guidance

1. Identify the formula for osmotic pressure: \(\Pi = iMRT\), where \(\Pi\) is the osmotic pressure, \(i\) is the van't Hoff factor, \(M\) is the molarity, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin.
2. Convert the temperature from Celsius to Kelvin by using the formula \(T(K) = T(°C) + 273.15\). For this problem, convert 37.0 °C to Kelvin.
3. Use the ideal gas constant \(R\) in units that match the pressure units in the problem. Since the pressure is given in atmospheres, use \(R = 0.0821 \text{ L atm K}^{-1} \text{mol}^{-1}\).
4. Assume the van't Hoff factor (\(i\)) for glucose is 1, because glucose does not dissociate into smaller particles in solution.
5. Solve the osmotic pressure formula for molarity \(M\) by rearranging it to \(M = \frac{\Pi}{iRT}\). Substitute the values of \(\Pi\), \(i\), \(R\), and \(T\) to find the molarity of the glucose solution.

Key Concepts

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the molarity of the solute particles in the solution, as described by the formula π = iCRT, where π is osmotic pressure, i is the van 't Hoff factor, C is molarity, R is the ideal gas constant, and T is temperature in Kelvin.

Van 't Hoff Factor (i)

The van 't Hoff factor (i) indicates the number of particles into which a solute dissociates in solution. For glucose, which does not dissociate, i equals 1. This factor is crucial for calculating osmotic pressure, as it affects the total concentration of solute particles contributing to the osmotic effect.

Ideal Gas Constant (R)

The ideal gas constant (R) is a fundamental constant used in various equations in chemistry, including those involving gases and osmotic pressure. Its value is typically 0.0821 L·atm/(K·mol). In the context of osmotic pressure, it helps relate the pressure, temperature, and molarity of the solution, allowing for the calculation of the required molarity to match a specific osmotic pressure.