The vapor pressure of a solution is directly related to the concentration of solute particles in the solution. To determine the molarity of the solution, we can use Raoult's Law, which states that the vapor pressure of an ideal solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.

Raoult's Law:
Psolution = Xsolvent * Psolvent

Where:
Psolution is the vapor pressure of the solution
Xsolvent is the mole fraction of the solvent
Psolvent is the vapor pressure of the pure solvent

In this case, the solute is glucose and the solvent is water. The vapor pressure of pure water at 100°C is 760 mmHg. The vapor pressure of the glucose solution is given as 710 mmHg.

Step 1: Calculate the mole fraction of water (solvent).
The mole fraction of a component is the ratio of the number of moles of that component to the total number of moles in the solution.

Mole fraction of water (Xwater) = moles of water / total moles

Since we are dealing with an aqueous solution of glucose, the total moles can be considered as the moles of water because glucose does not significantly contribute to the total moles. Therefore, Xwater = 1.

Step 2: Calculate the mole fraction of glucose (solute).
The mole fraction of glucose (Xglucose) = 1 - Xwater

Step 3: Apply Raoult's Law to find the mole fraction of water.
Psolution = Xwater * Psolvent
710 mmHg = 1 * 760 mmHg

Step 4: Calculate the molarity of the solution.
Molarity (M) is defined as the number of moles of solute per liter of solution.

Molarity (M) = moles of solute / volume of solution in liters

Since the mole fraction of glucose is equal to Xglucose, we can calculate the moles of glucose using the mole fraction and the molarity.

M = moles of glucose / volume of solution in liters

Since we are given the vapor pressure of the solution, we can assume that the solution is at its boiling point. At the boiling point, the mole fraction of the solvent is equal to its molar fraction. Therefore, we can use Xwater as the mole fraction of glucose.

Step 5: Calculate the molarity of the solution using the given information.

M = Xglucose * molality of the solution

Step 6: Substitute the values into the equation and calculate the molarity.

M = Xglucose * (mass of glucose / molar mass of glucose) / (mass of solvent / molar mass of water)

By substituting the values, we can calculate the molarity of the solution.