AVOGADRO'S LAW

Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) is a gas law which states that, under the same condition of temperature and pressure, equal volumes of all gases contain the same number of molecules. The law is named after Amedeo Avogadro who, in 1811,[1] hypothesized that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same number of molecules. Thus, the number of molecules or atoms in a specific volume of ideal gas is independent of their size or the molar mass of the gas.
As an example, equal volumes of molecular hydrogen and nitrogen contain the same number of molecules when they are at the same temperature and pressure, and observe ideal gas behavior. In practice, real gases show small deviations from the ideal behavior and the law holds only approximately, but is still a useful approximation for scientists. Avogadro's law is stated mathematically as: v = k n Where: V is the volume of the gas. n is the amount of substance of the gas. k is a proportionality constant. The most significant consequence of Avogadro's law is that the ideal gas constant has the same value for all gases. This means that: P1 V1 = p2 V2 = constant T1 N1 = T2 N2 Where: p is the pressure of the gas in the cell T is the temperature in kelvin of the gas 
Check out this video and solve the problems below.1. A 6.0 L sample at 25 °C and 2.00 atm of pressure contains 0.5 moles of a gas. If an additional 0.25 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas?
2: 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)? 3: A cylinder with a movable piston contains 2.00 g of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many grams of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.). 