A solution. Of glucose was prepared by dissolving certain amount in 100 grams of water ,the depression in freezing point is. 0.041kelvin if depression of water is 1.86 kelvin*kg/mol.calculate the weight of glucose dissolved .

dT = Kf*molality

You know dT and Kf, solve for m
m = mols/kg solvent. You know m and kg solvent, solve for mols.
mols = grams/molar mass. You know mols and molar mass, solve for grams.

To calculate the weight of glucose dissolved, we need to use the formula for depression in freezing point:

ΔT = Kf * m

Where:
ΔT = depression in freezing point (in Kelvin)
Kf = molal freezing point depression constant (in Kelvin kg/mol)
m = molality of the solution (in mol/kg)

Given that the depression in freezing point of water (ΔT) is 1.86 Kelvin*kg/mol and the depression in freezing point of the glucose solution is 0.041 Kelvin, we can calculate the molality (m) of the solution using the formula:

m = ΔT / Kf

Let's substitute the given values into the equation:

m = 0.041 Kelvin / 1.86 Kelvin*kg/mol

m ≈ 0.022 mol/kg

Now, we can calculate the weight of glucose dissolved using the formula:

weight of glucose = molality * mass of water

Given that the mass of water is 100 grams, we need to convert it to kilograms:

mass of water = 100 grams = 0.1 kg

Let's substitute the values into the equation:

weight of glucose = 0.022 mol/kg * 0.1 kg

weight of glucose ≈ 0.0022 mol

Therefore, the weight of glucose dissolved in the solution is approximately 0.0022 mol.

To calculate the weight of glucose dissolved in water, we can use the formula for depression in freezing point:

ΔTf = Kf * m

Where:
ΔTf = depression in freezing point
Kf = freezing point depression constant for the solvent
m = molality of the solution (moles of solute per kilogram of solvent)

In this case, the depression in freezing point (ΔTf) is given as 0.041 Kelvin. The depression of water (Kf) is given as 1.86 Kelvin*kg/mol.

Rearranging the formula, we can solve for the molality (m):

m = ΔTf / Kf

m = 0.041 / 1.86

m ≈ 0.02204 mol/kg

Now, we can calculate the weight of glucose using the following steps:

1. Determine the molar mass of glucose: This can be found in the periodic table or from a reliable source. The molar mass of glucose (C₆H₁₂O₆) is approximately 180.16 g/mol.

2. Calculate the weight of glucose:
Weight of glucose = m * molar mass * kg of water

Since the depression in freezing point was measured in 100 grams of water, we need to convert it to kilograms:

kg of water = 100 g / 1000 = 0.1 kg

Now, we can calculate the weight of glucose:

Weight of glucose = 0.02204 mol/kg * 180.16 g/mol * 0.1 kg

Weight of glucose ≈ 0.3963 grams

Therefore, the weight of glucose dissolved is approximately 0.3963 grams.