An aqueous solution contains 10% glucose by weight. Find the mole-fraction of both solute and solvent.
look at one kg of solution
100 g of glucose , and 900 g of water
100 g glucose = x moles
900 g water = y moles
total moles = x + y
glucose fraction = x / (x + y)
water fraction = y / (x + y)
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To find the mole fraction of solute and solvent in an aqueous solution containing 10% glucose by weight, we can follow these steps:
Step 1: Calculate the mass of the solute (glucose) and solvent (water):
Let's assume we have 100 grams of the solution. Since the solution is 10% glucose by weight, the mass of glucose is 10 grams and the mass of the water (solvent) is 90 grams.
Step 2: Convert the mass of the solute (glucose) to moles:
To convert grams to moles, we need to divide the mass of glucose by its molar mass. The molar mass of glucose (C6H12O6) is approximately 180.16 g/mol.
Moles of glucose = mass of glucose / molar mass of glucose
Moles of glucose = 10 g / 180.16 g/mol
Moles of glucose ≈ 0.0555 mol
Step 3: Calculate the mole fraction of solute (glucose):
The mole fraction (X) is calculated by dividing the moles of the solute (glucose) by the total moles of solute and solvent.
Mole fraction of glucose = moles of glucose / (moles of glucose + moles of water)
Mole fraction of glucose = 0.0555 mol / (0.0555 mol + 55.55 mol)
Mole fraction of glucose ≈ 0.001
Step 4: Calculate the mole fraction of water (solvent):
The mole fraction of water is obtained by subtracting the mole fraction of glucose from 1 since the mole fractions of all components of a solution add up to 1.
Mole fraction of water = 1 - mole fraction of glucose
Mole fraction of water = 1 - 0.001
Mole fraction of water ≈ 0.999
So, the mole fraction of glucose in the solution is approximately 0.001, and the mole fraction of water (solvent) is approximately 0.999.
To find the mole-fraction of both the solute and the solvent in the aqueous solution, we first need to calculate the mole-fraction of glucose (solute) and water (solvent) separately.
1. Mole-fraction of the solute (glucose):
To find the mole-fraction of glucose, we need to convert the weight percentage to moles. Given that the solution contains 10% glucose by weight, it means that for every 100 grams of the solution, 10 grams are glucose.
The molar mass of glucose (C6H12O6) is 180.16 g/mol. Therefore, we can calculate the number of moles of glucose using the formula:
Moles of glucose = (Weight of glucose / Molar mass of glucose)
In this case, the weight of glucose is 10 grams, so we have:
Moles of glucose = (10 g / 180.16 g/mol)
2. Mole-fraction of the solvent (water):
Since the solution is aqueous, the solvent is water. To calculate the mole-fraction of water, we need to determine its corresponding moles.
The molar mass of water (H2O) is 18.02 g/mol. We can calculate the number of moles of water using the formula:
Moles of water = (Weight of water / Molar mass of water)
Since the solution contains 10% glucose by weight, it means that the remaining 90% of the solution is water. Therefore, the weight of water is 90 grams.
Moles of water = (90 g / 18.02 g/mol)
Now that we have the moles of both solute and solvent, we can calculate their mole-fractions.
Mole-fraction of glucose = Moles of glucose / (Moles of glucose + Moles of water)
Mole-fraction of water = Moles of water / (Moles of glucose + Moles of water)
By substituting the calculated moles of glucose and water into the above formulas, you can find the mole-fractions of both solute and solvent in the given aqueous solution.