Suppose a salt and a glucose solution are separated by a membrane that is permeable to water but not to the solutes. The NaCl solution has a concentration of 1.95 g per 250 mL (molecular weight = 58.5). The glucose solution has a concentration of 9.0 g per 250 mL (molecular weight = 180).
Calculate the molality, millimolality, and milliosmolality of both solutions. State whether osmosis will occur and, if it will, in which direction. Explain your answer.
To calculate molality, we need to find the moles of solute per kilogram of solvent. Since water has a density of 1 g/mL, we can assume that there is 250 g of water in each 250 mL solution.
1. NaCl Solution:
Mass of NaCl = 1.95 g
Molecular weight of NaCl = 58.5 g/mol
Moles of NaCl = (mass of NaCl) / (molecular weight of NaCl) = 1.95 g / 58.5 g/mol ≈ 0.0333 mol
Molality (m) = moles of solute / kg of solvent = 0.0333 mol / 0.250 kg = 0.133 mol/kg
Millimolality (mm) = molality × 10^3 = 0.133 mol/kg × 10^3 = 133 mmol/kg
2. Glucose Solution:
Mass of glucose = 9.0 g
Molecular weight of glucose = 180 g/mol
Moles of glucose = (mass of glucose) / (molecular weight of glucose) = 9.0 g / 180 g/mol ≈ 0.050 mol
Molality (m) = moles of solute / kg of solvent = 0.050 mol / 0.250 kg = 0.200 mol/kg
Millimolality (mm) = molality × 10^3 = 0.200 mol/kg × 10^3 = 200 mmol/kg
Now, we will calculate the milliosmolality, which is a measure of the total concentration of all particles in the solution, taking into account that NaCl will dissociate into two particles (Na+ and Cl-) when dissolved in water.
3. NaCl Solution:
Milliosmolality (mosm) = millimolality × number of particles = 133 × 2 = 266 mosm/kg
4. Glucose Solution:
Milliosmolality (mosm) = millimolality × number of particles = 200 × 1 = 200 mosm/kg
Now, let's determine the direction of osmosis:
Osmosis occurs from solutions with a lower concentration of solute particles (higher water potential) to solutions with higher concentration of solute particles (lower water potential).
Here, the glucose solution has a milliosmolality of 200 mosm/kg, while the NaCl solution has a milliosmolality of 266 mosm/kg.
Therefore, osmosis will occur from the glucose solution to the NaCl solution, as water will move from a lower concentration of solute particles to a higher concentration.
To calculate the molality, millimolality, and milliosmolality of both solutions, we'll need to start by finding the number of moles of each solute.
1. Molality:
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, the solvent is water.
For the NaCl solution:
Mass of NaCl = 1.95 g
Molecular weight of NaCl = 58.5 g/mol
Volume of solution = 250 mL = 0.25 L
Number of moles of NaCl = mass / molecular weight = 1.95 g / 58.5 g/mol = 0.033 mol
Mass of water = volume of solution = 0.25 L = 250 g (as the density of water is approximately 1 g/mL)
Molality (m) = moles of solute / mass of water in kg = 0.033 mol / 0.25 kg = 0.132 mol/kg
For the glucose solution:
Mass of glucose = 9.0 g
Molecular weight of glucose = 180 g/mol
Volume of solution = 250 mL = 0.25 L
Number of moles of glucose = mass / molecular weight = 9.0 g / 180 g/mol = 0.05 mol
Mass of water = volume of solution = 0.25 L = 250 g
Molality (m) = moles of solute / mass of water in kg = 0.05 mol / 0.25 kg = 0.2 mol/kg
2. Millimolality:
Millimolality is the same as molality, but the mole unit is multiplied by 1000.
Millimolality = Molality (m) * 1000
For the NaCl solution:
Millimolality = 0.132 mol/kg * 1000 = 132 millimol/kg
For the glucose solution:
Millimolality = 0.2 mol/kg * 1000 = 200 millimol/kg
3. Milliosmolality:
Milliosmolality is a measure of the number of solute particles per kilogram of solvent. Since NaCl dissociates into two ions (Na+ and Cl-), and glucose does not dissociate, we need to take this into account.
For the NaCl solution:
Number of solute particles per mole = 2 (because NaCl dissociates into Na+ and Cl- ions)
Milliosmolality = Molality (m) * number of solute particles per mole * 1000
Milliosmolality = 0.132 mol/kg * 2 * 1000 = 264 milliosmol/kg
For the glucose solution:
Milliosmolality = Molality (m) * 1000 (since glucose does not dissociate)
Milliosmolality = 0.2 mol/kg * 1000 = 200 milliosmol/kg
Osmosis will occur when there is a difference in solute concentration on either side of a semipermeable membrane. In this case, since the glucose solution has a higher molality, millimolality, and milliosmolality compared to the NaCl solution, the osmosis will occur from the glucose solution to the NaCl solution. Water molecules will move from an area of lower solute concentration (glucose solution) to an area of higher solute concentration (NaCl solution) to balance the concentrations.
To calculate the molality of a solution, we need to find the moles of solute per kilogram of solvent.
For the NaCl solution:
Mass of NaCl = 1.95 g
Molecular weight of NaCl = 58.5 g/mol
Volume of NaCl solution = 250 mL = 0.25 L
First, let's calculate the moles of NaCl:
moles of NaCl = mass of NaCl / molecular weight of NaCl = 1.95 g / 58.5 g/mol = 0.0333 mol
Now, let's find the mass of water in the solution:
Mass of water = volume of NaCl solution * density of water = 0.25 L * 1000 g/L = 250 g
Now, we can calculate the molality of the NaCl solution:
molality of NaCl = moles of NaCl / mass of water (in kg) = 0.0333 mol / 0.250 kg = 0.133 mol/kg
For the glucose solution:
Mass of glucose = 9.0 g
Molecular weight of glucose = 180 g/mol
Volume of glucose solution = 250 mL = 0.25 L
First, let's calculate the moles of glucose:
moles of glucose = mass of glucose / molecular weight of glucose = 9.0 g / 180 g/mol = 0.05 mol
Now, we can calculate the molality of the glucose solution:
molality of glucose = moles of glucose / mass of water (in kg) = 0.05 mol / 0.250 kg = 0.2 mol/kg
Millimolality is the same as molality, but multiplied by 1000. So in this case:
millimolality of NaCl = 0.133 mol/kg * 1000 = 133 mmol/kg
millimolality of glucose = 0.2 mol/kg * 1000 = 200 mmol/kg
Milliosmolality is the same as molality, but multiplied by the molecular weight of the solute. So in this case:
milliosmolality of NaCl = 0.133 mol/kg * 58.5 g/mol * 1000 = 7798 mOsm/kg
milliosmolality of glucose = 0.2 mol/kg * 180 g/mol * 1000 = 36,000 mOsm/kg
Now, let's determine whether osmosis will occur and in which direction. Osmosis is the movement of solvent molecules from an area of lower solute concentration to an area of higher solute concentration through a semipermeable membrane. In this case, the membrane is permeable to water but not to the solutes (salt and glucose).
The NaCl solution has a lower concentration compared to the glucose solution. Therefore, water molecules will move from the NaCl solution (lower solute concentration) to the glucose solution (higher solute concentration) through the membrane by osmosis. So, osmosis will occur from the NaCl solution to the glucose solution.