Answer:
1) 0.18106 M is the molarity of the resulting solution.
2) 0.823 Molar is the molarity of the solution.
Explanation:
1) Volume of stock solution = 
Concentration of stock solution = 
Volume of stock solution after dilution = 
Concentration of stock solution after dilution = 
( dilution )

0.18106 M is the molarity of the resulting solution.
2)
Molarity of the solution is the moles of compound in 1 Liter solutions.

Mass of potassium permanganate = 13.0 g
Molar mass of potassium permangante = 158 g/mol
Volume of the solution = 100.00 mL = 0.100 L ( 1 mL=0.001 L)

0.823 Molar is the molarity of the solution.
Answer: It decreases because nonvolatile aluminum and chloride ions now occupy some of the volume of the system.
Explanation:
Vapor pressure of a liquid is defined as the pressure exerted by the vapors in equilibrium with the liquid/solution at a particular temperature.
So, when a non-volatile solute is added to a solvent then its molecules align at the surface of liquid. As a result, less number of solvent molecules will escape from the solution. Thus, there will be decrease in vapors and thus the vapor pressure decrease.
The relative lowering of vapor pressure is directly proportional to the amount of dissolved solute.
You didn’t show the cylinder containing water, so I created one that you can use as a model (see image).
The water level was originally at 37 mL.
Then you added the ball, and it displaced its volume of water.
The new volume reading is 52 mL, so
Volume of ball = volume of displaced water = 52 mL – 37 mL = 15 mL.