To find the molarity of the solution, we need to use the given information about the mass of solute and the volume of the solution.
First, we need to determine the volume of the solution. We are given the mass of the solvent (water) and its density. Using the formula:
volume = mass / density
We can calculate the volume of water by dividing the given mass of 100 g by the density of 1.34 g/mL.
volume = 100 g / 1.34 g/mL = 74.63 mL
Next, we need to convert the volume of water to liters, as molarity is expressed in moles per liter (mol/L).
volume = 74.63 mL / 1000 mL/L = 0.07463 L
Now, we can calculate the number of moles of sucrose (solute) that dissolved in the given amount of water.
moles of sucrose = mass of sucrose / molar mass of sucrose
The mass of sucrose is given as 211.4 g, and the molar mass of sucrose is 342 g/mol.
moles of sucrose = 211.4 g / 342 g/mol = 0.618 mol
Finally, we can use the number of moles of sucrose and the volume of the solution to calculate the molarity using the formula:
molarity = moles of solute / volume of solution
Substituting the values, we have:
molarity = 0.618 mol / 0.07463 L = 8.29 mol/L
Therefore, the molarity of the sucrose solution is 8.29 mol/L.