Avogadros Law Example Problem

Avogadros Law Example Problem Avogadros gas law states the volume of a gas is proportional to the number of moles of gas present when the temperature and pressure are held constant. This example problem demonstrates how to use Avogadros law to determine the volume of a gas when more gas is added to the system. Avogadro's Law Equation Before you can solve any problem regarding Avogadros gas law, its important to review the equation for this law. There are a few ways to write this  gas law, which is a mathematical relation. It may be stated: k V/n Here, k is a proportionality constant, V is the volume of a gas, and n is the number of moles of a gas. Avogadros law also means the ideal gas constant is the same value for all gases, so: constant p1V1/T1n1   P2V2/T2n2V1/n1   V2/n2V​1n2   V2n1 where p is pressure of a gas, V is volume, T is temperature, and n is number of moles. Avogadro's Law Problem A 6.0 L sample at 25 °C and 2.00 atm of pressure contains 0.5 mole of a gas. If an additional 0.25 mole of gas at the same pressure and temperature are added, what is the final total volume of the gas? Solution First, express Avogadros law by its  formula: Vi/ni Vf/nfwhereVi initial volumeni initial number of molesVf final volumenf final number of moles For this example, Vi 6.0 L and ni 0.5 mole. When 0.25 mole is added: nf ni 0.25 molenf 0.5 mole 0.25 molenf 0.75 mole The only variable remaining is the final volume. Vi/ni Vf/nf Solve for Vf Vf ​ Vinf/niV​f (6.0 L x 0.75 mole)/0.5 moleVf 4.5 L/0.5 Vf 9 L Check to see if the answer makes sense. You would expect the volume to increase if more gas is added. Is the final volume greater than the initial volume? Yes. Doing this check is useful because it is easy to put the initial number of moles in the numerator and the final number of moles in the denominator. If this had happened, the final volume answer would have been smaller than the initial volume. Thus, the final volume of the gas is 9.0 Notes Regarding Avogadro's Law Unlike Avogadros number, Avogadros law was actually proposed by   Amedeo Avogadro. In 1811, he hypothesized two samples of an ideal gas with the same volume and at the same pressure and temperature contained the same number of molecules.Avogadros law is also called Avogadros principle or Avogadros hypothesis.Like the other ideal gas laws, Avogadros law only approximates the behavior of real gases. Under conditions of high temperature or pressure, the law is inaccurate. The relation works best for gases held at low pressure and ordinary temperatures. Also, smaller gas particles- helium, hydrogen, and nitrogen- yield better results than larger molecules, which are more likely to interact with each other.Another mathematical relation used to express Avogadros law is: V/n k Here, V is the volume, n is the number of moles of the gas, and k is the proportionality constant. Its important to note this means the ideal gas constant is the same for all gases.