Question

What is the water potential of a 0.5 m sucrose solution at 21 degrees celsius in an open system?

Answer 1

The water potential of a 0.5 M sucrose solution at 21 degrees Celsius in an open system is approximately -6.112 atm.

Step-by-step explanation:

The water potential of a solution measures the tendency of water to move from one area to another. It is affected by various factors such as solute potential, pressure potential, and temperature. In an open system, the water potential is equal to the solute potential. The formula to calculate water potential is:

Water potential (ψ) = Solute potential (ψs)

For a 0.5 M sucrose solution at 21 degrees Celsius, you need to determine the solute potential. The solute potential of a solution can be calculated using the formula:

Solute potential (ψs) = -cRT

Where:
c = concentration in mol/L
R = gas constant (0.0831 L•atm/mol•K)
T = temperature in Kelvin

Convert the temperature from Celsius to Kelvin by adding 273.15: 21 + 273.15 = 294.15 K

Now, plug in the values into the formula:

Solute potential (ψs) = -(0.5)(0.0831)(294.15)

Solute potential (ψs) ≈ -6.112 atm

Answer 2

The water potential of a 0.5 m sucrose solution at 21 degrees Celsius in an open system is the sum of its solute potential and pressure potential. The pressure potential is zero in an open system; thus, the water potential equals the solute potential calculated using the formula Ψs = -iCRT.

Step-by-step explanation:

The water potential of a 0.5 m sucrose solution in an open system at 21 degrees Celsius can be defined as the potential energy of water in that solution compared to pure water. Water potential is comprised of solute potential (Ψs) and pressure potential (Ψp), where the pressure potential in an open system is zero.

To calculate the solute potential, we can use the formula Ψs = -iCRT, where 'i' is the ionization constant (which is 1 for sucrose, as it does not ionize), 'C' is the molar concentration of the solution, 'R' is the ideal gas constant (0.0831 liter bar per mole K), and 'T' is the temperature in Kelvin. However, to find the exact value of the water potential, we both need the solute potential and know that the pressure potential (Ψp) in an open system equals zero. Therefore, the overall water potential is equal to the solute potential.

Without the exact numerical values for the constants and temperature conversion to Kelvin for this specific scenario, we cannot calculate the precise water potential, but the process involves taking the concentration (0.5 m), converting the temperature to Kelvin, and plugging these values into the formula.