Question

Combined Gas Relationship Since the Ideal Gas Law produces a constant (R), it can be used to look at a gas sample in which initial and final conditions have changed. The combined gas relationship is as follows P.V R=P.V2 n, T n2 T2 where P, Vi,and T, and n, are the initial pressure, volume, temperature, and number of moles of gas. The final conditions are represented by P, V2, T2 and n2. If any of the conditions in the initial and final state of the gas are unchanged, they can be mathematically cancelled out of the equation. The name "combined" gas law comes from the fact that several other gas laws can be combined to make this law (Boyle's Law, Charles' Law, and Gay-Lussac's Law). Each of these laws can be derived by holding one variable constant. For example, Boyles Law characterizes the relationship between pressure and volume of a sample of gas at constant temperature. If T, T2, these two variables (and "n") will cancel and the resulting equation will be will result in an increase in pressure. In other words the properties of pressure and volume have an inverse relationship. Prove this statement by solving the problem below. P,V PV2. This law tells us that a decrease in volume The air in a 10.0 L tank has a pressure of 1.2 atm. What is the new pressure of the air when the air is placed in a 5.0 L tank. Assume that the temperature remains constant Avogadro's Law - In 1811, Amedeo Avogadro stated that the volume of gas is directly related to the number of moles of gas when the temperature and pressure are not changed. Derive Avogadro's Law from this information, and the combined gas relationship described above. For example, if the number of moles of a gas are doubled, then the volume will double as long as the pressure and temperature are not changed. The problem below illustrates Avogadro's Law A balloon contains 3.5 moles of helium and has a volume of 6.0 L. What will the new balloon volume be if 5.0 moles of helium are added to the balloon? Show your work.

Answer 1

A from the above, Boyle's law we get- pri = Pz V₂ where, p = initial pressure = 1.2 atm " - initial volume = 10.0L P2 = 2= final pressure final volume = 58.02. so, P2.2 = 1249 = 12 atm x 104 1. SK 32 = 2.4 atm As from the Boyle's law pat. So, here volume decreases and hence press- ure increases, so the above statement is correct. Scanned with (page-1) CamScanner

Amedeo Avogardo Stated that the volume of gas is directly related to the number of moles of gases when temperature and pressure are not change. Let, volume of gas is'v' and more of the gas is 'n . So, from the Avogardo statement we can write a won when P and? are constant] . In the above PV, int, RBV2 R = п, та So, we will replacce we inters of me : SR - :. R = RDP so, from the Avogardo we can write. van, V, α η. Now, V = initial volume =6L V₂ = final volume : n = initial mole = 3-5 moles m2 = final mole so moles. & V2 = 27 xv, 215x6 z = 8.5741 New ballon volume will be CamScanner