Solutions

Step 1: Molarity of water.
Molarity is the number of moles of solute per liter of solution. The molarity of pure water is calculated as follows:
- Molarity = .
- Given that water's molar mass is and its density is approximately , we calculate the molarity as:

Step 2: Conclusion.
Thus, the molarity of water is 55.56 mol/litre.

Step 1: Formula for osmotic pressure.
Osmotic pressure ( ) is the pressure required to stop osmosis. The formula is derived from the ideal gas law and given by: where:
- is the number of moles of solute,
- is the gas constant,
- is the temperature in Kelvin,
- is the volume of the solution.

Step 2: Conclusion.
The correct formula for osmotic pressure is , which corresponds to option (1).

Step 1: Definition of Mole Fraction.
Mole fraction is the ratio of the number of moles of a component to the total number of moles of all components in the mixture. It is represented as: where is the mole fraction of component , is the number of moles of component , and is the total number of moles of all components in the mixture.

Step 2: Conclusion.
Mole fraction is a unitless quantity and is often used in the calculation of colligative properties.

Step 1: Definition of Solution.
A solution is a homogeneous mixture of two or more substances. In a solution, one substance is dissolved in another, with the substance present in the greater amount being the solvent, and the substance present in the lesser amount being the solute.

Step 2: Conclusion.
Solutions can be in any phase: solid, liquid, or gas. Common examples include salt dissolved in water (aqueous solution) or air (gas solution).

Step 1: Use the formula for boiling point elevation.
The boiling point elevation is given by: where: - is the change in boiling point, - is the ebullioscopic constant for water (0.52 K kg mol ), - is the molality of the solution.

Step 2: Calculate the molality.
Molality is given by: The moles of glucose is: Since the mass of water is 1 kg, the molality is:

Step 3: Calculate the change in boiling point.

Step 4: Calculate the boiling point.
The boiling point of water is 100°C at 1 atm. The boiling point at 1.013 bar is:

Step 5: Conclusion.
Thus, the boiling point of the solution at 1.013 bar is 100.052°C.

Step 1: Use Raoult's Law.
Raoult's law states that the reduction in vapour pressure is proportional to the mole fraction of the solute in the solution: where: - is the vapour pressure of pure benzene (0.850 bar), - is the vapour pressure of the solution (0.845 bar), - is the mole fraction of the solute.

Step 2: Calculate the mole fraction of the solute.
The decrease in vapour pressure is: From Raoult's law:

Step 3: Calculate the moles of benzene.
The number of moles of benzene is:

Step 4: Calculate the moles of solute.
The mole fraction is also equal to: Substitute the values: Solving for :

Step 5: Calculate the molar mass of the solute.
The molar mass of the solute is:

Step 6: Conclusion.
Thus, the molar mass of the solid substance is approximately 169.9 g/mol.