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
(assume volume is same for both solns)
How much of solution 1 is mixed with how much of solution 2. Won't it make a differen
First, the formula for sucrose is C12H22O11.
For the 0.1495 M soln.
density = 1.018 g/mL so 1 L has a mass of
1.018 g/mL x 1000 mL = 1018 grams.
How much sucrose is in that?
0.1495 moles x molar mass sucrose = 0.1495 x 342 (approximately, you look it up and do the calculations more accurately). = 51.1 grams C12H22O11.
mass water = 1018-51.1 = ?? g H2O.
For the 12.00% by mass solution.
density = 1.038 g/mL. Mass of 1L of this solution is 1.038 g/mL x 1000 mL = 1038 grams for the solution.
12% of that is sucrose; therefore
1038 x 0.12 = 124.6 g C12H22O11(again, I've rounded here and there).
mass water = 1038-51.6 = ?? g H2O
I don't think we can go any further until we know how much of each solution was mixed to form the final solution. Or have I missed something?
Step 1: Calculate the mass of sucrose in the first solution.
Given:
Molarity of the first solution (M1) = 0.1495 M
Density of the first solution (d1) = 1.018 g/mL
To calculate the mass, we need to use the formula:
mass = volume x density
Since the volume is not given, but we are assuming it is the same for both solutions, we can ignore it since it will cancel out when calculating the moles. So we can write:
mass1 = d1
Therefore, the mass of sucrose in the first solution is 1.018 g/mL.
Step 2: Calculate the mass of sucrose in the second solution.
Given:
Mass percent of sucrose in the second solution = 12.00%
Density of the second solution (d2) = 1.038 g/mL
To calculate the mass of sucrose, we first need to calculate the total mass of the second solution. Since we know the mass percent, we can calculate it using the formula:
mass% = (mass of component / total mass) x 100
Let's assume the total mass of the second solution is 100 g, so we can write:
12.00% = (mass of sucrose / 100 g) x 100
Solving for the mass of sucrose, we get:
mass of sucrose = (12.00 / 100) x 100 g
Therefore, the mass of sucrose in the second solution is 12.00 g.
Step 3: Calculate the total mass of the mixed solution.
Since we assumed the volume is the same for both solutions, and the density is given for each solution, we can calculate the total mass by adding the individual masses of the solutions, as follows:
total mass = mass1 + mass2
Using the values we calculated in Step 1 and Step 2, we have:
total mass = 1.018 g/mL + 12.00 g
Therefore, the total mass of the mixed solution is the sum of these values.
Step 4: Calculate the moles percent of sucrose in the mixed solution.
To calculate the moles percent, we need to determine the number of moles of sucrose in the mixed solution. To do this, we use the equation:
moles = mass / molar mass
The molar mass of sucrose (C12H22O12) is:
12(12.01 g/mol) + 22(1.01 g/mol) + 12(16.00 g/mol) = 342.30 g/mol
Using the total mass and molar mass, we have:
moles of sucrose = total mass / molar mass
Finally, the moles percent can be calculated by using the formula:
moles percent = (moles of sucrose / total moles) x 100
Since the total volume of the mixed solution is assumed to be the same for both solutions, the total moles of the mixed solution will be the same as the moles of sucrose calculated. So, the moles percent will be 100%.
Therefore, the moles percent of sucrose in the mixed solution is 100%.
To calculate the moles of C12H22O12 in the mixed solution, follow these steps:
Step 1: Calculate the mass of each solution.
- For the first solution: Mass1 = Volume1 * Density1
- For the second solution: Mass2 = Volume2 * Density2
Since the volume is assumed to be the same for both solutions, we can let Volume1 = Volume2 = V. Therefore, Mass1 and Mass2 can be calculated using the given densities.
Step 2: Calculate the mass of sucrose in each solution.
- For the first solution: Mass_sucrose1 = Mass1 * (0.1495 M)
- For the second solution: Mass_sucrose2 = Mass2 * (12.00 %)
Step 3: Convert the mass of sucrose to moles.
- Moles_sucrose1 = Mass_sucrose1 / molar mass of sucrose
- Moles_sucrose2 = Mass_sucrose2 / molar mass of sucrose
The molar mass of sucrose (C12H22O12) can be calculated by summing the atomic masses of its constituent elements.
Step 4: Calculate the total moles of sucrose in the mixed solution.
- Total_moles_sucrose = Moles_sucrose1 + Moles_sucrose2
Step 5: Calculate the moles percent of C12H22O12 in the mixed solution.
- Moles_percent_C12H22O12 = (Total_moles_sucrose / Total volume of the mixed solution) * 100
Note: The total volume of the mixed solution is the sum of the volumes of the two initial solutions, which we assumed to be the same.