Two aqueous solutions of sucrose, C12H22O12, are mixed. One solution is 0.1495 M sucrose and has d = 1.018 g/mL; the other is 12.00 sucrose by mass and has d = 1.038 g/ml.
Calculate the moles C12H22O12 percent in the mixed solution.
Please provide steps
To calculate the moles of C12H22O12 percent in the mixed solution, you need to follow these steps:
Step 1: Convert the density (d) values to mass (m) values.
The mass can be calculated using the formula: mass = density × volume.
For the first solution: mass = 1.018 g/mL × 1 L = 1018 g.
For the second solution: mass = 1.038 g/mL × 1 L = 1038 g.
Step 2: Calculate the moles of sucrose in each solution.
The moles can be calculated using the equation: moles = mass / molar mass.
The molar mass of sucrose (C12H22O12) is calculated by adding up the atomic masses of carbon, hydrogen, and oxygen:
12 carbon atoms × 12.01 g/mol + 22 hydrogen atoms × 1.01 g/mol + 11 oxygen atoms × 16.00 g/mol = 342.3 g/mol.
For the first solution: moles = mass / molar mass = 1018 g / 342.3 g/mol = 2.976 mol.
For the second solution: moles = mass / molar mass = 1038 g / 342.3 g/mol = 3.032 mol.
Step 3: Calculate the total moles of sucrose in the mixed solution.
Since the two solutions are mixed, you simply add the moles from each solution together.
Total moles = moles of first solution + moles of second solution = 2.976 mol + 3.032 mol = 6.008 mol.
Step 4: Calculate the moles C12H22O12 percent in the mixed solution.
To calculate the moles C12H22O12 percent, you need to calculate the moles percent by mass.
The moles percent by mass can be calculated using the following formula:
Moles percent by mass = (moles of solute / total moles of solution) × 100.
In this case, the moles of solute (sucrose) is the total moles calculated in Step 3, which is 6.008 mol.
The total moles of solution is the sum of the moles of both solutions, which is 2.976 mol + 3.032 mol = 6.008 mol.
Moles percent by mass = (6.008 mol / 6.008 mol) × 100 = 100%.
Therefore, the moles of C12H22O12 percent in the mixed solution is 100%.