Problem 14 - Chemistry: An Atoms-Focused Approach

Question

How is the osmotic pressure of a solution related to its molar concentration and its temperature?

Step-by-Step Solution

Answer

Answer: The osmotic pressure of a solution is directly proportional to its molar concentration and temperature, as described by the modified van't Hoff equation: π = CRT. As the molar concentration or the temperature of the solution increases, the osmotic pressure also increases.

Step 1: Identifying the van't Hoff equation

To find the relationship between osmotic pressure, molar concentration, and temperature, we will use the van't Hoff equation. The equation is given by: π = (n/V)RT where π is the osmotic pressure, n is the number of moles of solute, V is the volume of the solution in liters, R is the ideal gas constant (0.0821 L atm K⁻¹ mol⁻¹), and T is the temperature in Kelvin.

Step 2: Connecting van't Hoff equation with molar concentration

The molar concentration (C) of solute in a solution is defined as the number of moles of solute (n) per unit volume (V) of the solution in liters. It is given by: C = n/V By substituting this expression in the van't Hoff equation, we get: π = CRT

Step 3: Impact of temperature on osmotic pressure

From the modified van't Hoff equation (π = CRT), we can see that the osmotic pressure is directly proportional to temperature (T). This means that as the temperature increases, the osmotic pressure of the solution also increases and vice versa.

Step 4: Conclusion

The osmotic pressure of a solution is directly proportional to its molar concentration and temperature, as described by the modified van't Hoff equation: π = CRT As the molar concentration or the temperature of the solution increases, so does the osmotic pressure.