At 25 °C, the density of a 40.0% (m/m) solution of sucrose, C12H22O11, in water is 1.18 g/mL. What is the molarity of this solution?
40% is 40 g sucrose/100 g solution.
Use density to convert 100 g solution to volume in cc and convert that to L.
Convert 40 g sucrose to mols. mol = grams/molar mass.
Then M = mols/L
To find the molarity of the solution, we need to know the number of moles of sucrose (C12H22O11) present in the given solution.
To calculate the number of moles, we can use the formula:
Number of moles = Mass / Molar mass
First, let's calculate the mass of the solution. The density of the solution is given as 1.18 g/mL. Assuming we have 1 mL of the solution, the mass of the solution will be:
Mass of the solution = Volume * Density
Mass of the solution = 1 mL * 1.18 g/mL
Mass of the solution = 1.18 g
Next, we need to determine the mass of sucrose in the solution. The solution is described as a 40.0% (m/m) solution, which means that 40.0 g of sucrose is present in 100 g of the solution.
Mass of sucrose = (40.0% / 100%) * Mass of the solution
Mass of sucrose = (40.0 / 100) * 1.18 g
Mass of sucrose = 0.472 g
The molar mass of sucrose (C12H22O11) can be found using the atomic masses of carbon (C), hydrogen (H), and oxygen (O):
Molar mass of sucrose = (12.01 g/mol * 12) + (1.01 g/mol * 22) + (16.00 g/mol * 11)
Molar mass of sucrose = 144.12 g/mol + 22.22 g/mol + 176.00 g/mol
Molar mass of sucrose = 342.34 g/mol
Now, we can calculate the number of moles of sucrose in the solution:
Number of moles = Mass of sucrose / Molar mass of sucrose
Number of moles = 0.472 g / 342.34 g/mol
Number of moles = 0.00138 mol
Finally, we can find the molarity of the solution by dividing the number of moles of sucrose by the volume of the solution in liters:
Molarity = Number of moles / Volume of solution (in liters)
Molarity = 0.00138 mol / 0.001 L
Molarity = 1.38 mol/L
Therefore, the molarity of this solution is 1.38 mol/L.