Question

an aqueous solution of fructose (mm = 180.2 g/mol) has a molality of 4.87 m and a density of 1.30 g/ml. what is the molarity of fructose in the solution?

Answer 1

To find the molarity of the fructose solution, we first need to calculate the mass of the solvent (water) in the solution. Then, we can calculate the number of moles of fructose present in the solution using the molality. Finally, we divide the number of moles of fructose by the volume of the solution to find the molarity.

Step-by-step explanation:

The molarity of a solution is defined as the number of moles of solute present in 1 liter of solution. In this case, we have the molality of the fructose solution, which is given as 4.87 m. To find the molarity, we need to convert the molality to moles of fructose per liter of solution.

First, we need to calculate the mass of the solvent (water) present in 1 liter of the solution. Since the density of the solution is given as 1.30 g/ml, the mass of 1 liter of the solution would be 1.30 kg. Therefore, the mass of water in 1 liter of the solution is:

mass of water = density of water × volume of water = 1.30 g/ml × 1000 ml = 1300 g = 1.30 kg

Next, we can calculate the number of moles of fructose present in the solution:

moles of fructose = molality × mass of solvent (in kg) = 4.87 m × 1.30 kg = 6.331 moles

Finally, to find the molarity, we divide the number of moles of fructose by the volume of the solution (1 liter):

molarity = moles of fructose / volume of solution = 6.331 moles / 1 liter = 6.331 M

Answer 2

The molarity of fructose in the solution is
`\(4.76 \, \text{M}\)`.

To find the molarity M from molality m, you can use the following formula:

`\[ M = (m)/(1 + (V * \rho / 1000)) \]`

where:

• m is the molality of the solution,

• V is the molar volume of water (which is approximately 18 mL/mol),

• 
  `\( \rho \)` is the density of the solution in g/mL.

Given that the molality m is 4.87 m, the density is 1.30 g/mL, and the molar volume V is 18 mL/mol, we can substitute these values into the formula.

`\[ M = (4.87)/(1 + (18 * 1.30 / 1000)) \]`

Now, calculate the molarity. Ensure that all units are consistent.

`\[ M = (4.87)/(1 + (0.0234)) \]`

`\[ M \approx (4.87)/(1.0234) \]`

`\[ M \approx 4.76 \, \text{M} \]`

Therefore, the molarity of fructose in the solution is approximately
`\(4.76 \, \text{M}\)`.