Calculate the mole fraction of glucose (C6H12O6) in a solution which contains 15g of glucose in 100 g of H2O.
mol glucose = grams/molar mass
mol H2O = grams/molar mass
Xglucose = n glucose/total mols.
XH2O = n H2O/total mols.
To calculate the mole fraction of glucose (C6H12O6) in a solution, you'll need to determine the moles of glucose and water separately.
Step 1: Calculate the moles of glucose (C6H12O6):
Given:
Mass of glucose = 15g
To convert grams to moles, we need the molar mass of glucose:
Molar mass of glucose (C6H12O6) =
(6 * atomic mass of carbon) + (12 * atomic mass of hydrogen) + (6 * atomic mass of oxygen)
= (6 * 12.01 g/mol) + (12 * 1.01 g/mol) + (6 * 16.00 g/mol)
= 72.06 g/mol + 12.12 g/mol + 96.00 g/mol
= 180.18 g/mol
Now, use the formula:
Number of moles = Given mass / Molar mass
Number of moles of glucose = 15g / 180.18 g/mol
Step 2: Calculate the moles of water (H2O):
Given:
Mass of water = 100g
The molar mass of water (H2O) = (2 * atomic mass of hydrogen) + atomic mass of oxygen
= (2 * 1.01 g/mol) + 16.00 g/mol
= 2.02 g/mol + 16.00 g/mol
= 18.02 g/mol
Number of moles of water = 100g / 18.02 g/mol
Step 3: Calculate the mole fraction of glucose:
Mole fraction of glucose = moles of glucose / (moles of glucose + moles of water)
Now you just need to substitute the values calculated in steps 1 and 2 into the formula:
Mole fraction of glucose = moles of glucose / (moles of glucose + moles of water)
Mole fraction of glucose = (15g / 180.18 g/mol) / [(15g / 180.18 g/mol) + (100g / 18.02 g/mol)]
To calculate the mole fraction of glucose in the solution, you need to know the number of moles of glucose and water in the solution.
1. Calculate the number of moles of glucose:
- The molar mass of glucose (C6H12O6) is: 6*(12.01 g/mol) + 12*(1.01 g/mol) + 6*(16.00 g/mol) = 180.18 g/mol
- The number of moles of glucose is: 15 g / 180.18 g/mol = 0.0832 mol
2. Calculate the number of moles of water:
- The molar mass of water (H2O) is: 2*(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol
- The number of moles of water is: 100 g / 18.02 g/mol = 5.551 mol
3. Calculate the mole fraction of glucose:
- The mole fraction of glucose is the ratio of the number of moles of glucose to the total number of moles in the solution.
- The total number of moles is: 0.0832 mol + 5.551 mol = 5.634 mol
- The mole fraction of glucose is: 0.0832 mol / 5.634 mol = 0.0147 (rounded to four decimal places)
Therefore, the mole fraction of glucose in the solution is approximately 0.0147.