Combined Gas Law Definition and Examples

Combined Gas Law Definition and Examples The combined gas law combines the three gas laws: Boyles Law, Charles Law, and Gay-Lussacs Law. It states that the ratio of the product of pressure and volume and the absolute temperature of a gas is equal to a constant. When Avogadros law is added to the combined gas law, the ideal gas law results. Unlike the named gas laws, the combined gas law doesnt have an official discoverer. It is simply a combination of the other gas laws that works when everything except temperature, pressure, and volume are held constant. There are a couple of common equations for writing the combined gas law. The classic law relates Boyles law and Charles law to state: PV/T k where P pressure,  V volume,  T absolute temperature (Kelvin), and  k constant. The constant k is a true constant if the number of moles of the gas doesnt change.  Otherwise, it varies. Another common formula for the combined gas law relates before and after conditions of a gas: P1V1 / T1 P2V2 / T2 Example Find the volume of a gas at STP when 2.00 liters is collected at 745.0 mm Hg and 25.0 degrees Celsius. To solve the problem, you first need to identify which formula to use. In this case, the question asks about conditions at STP, so you know youre dealing with a before and after problem. Next, you need to understand  STP. If you havent memorized this already (and you probably should, since it appears a lot), STP refers to standard temperature and pressure, which is 273 Kelvin and 760.0 mm Hg. Because the law works using absolute temperature, you need to convert  25.0  degrees Celsius to the Kelvin scale. This gives you 298 Kelvin. At this point, you can plug the values into the formula and solve for the unknown. A common mistake some people make when theyre new to this kind of problem is confusing which numbers go together. Its good practice to identify the variables. In this problem they are: P1   745.0 mm HgV1   2.00 LT1   298 KP2   760.0 mm HgV2   x (the unknown youre solving for)T2   273 K Next, take the formula and set it up to solve for the unknown  x, which in this problem  is  V2: P1V1  / T1   P2V2  / T2 Cross-multiply to clear the fractions: P1V1T2   P2V2T1 Divide to isolate  V2: V2   (P1V1T2) / (P2T1) Plug in the numbers and solve for V2: V2  Ã‚  (745.0 mm Hg  · 2.00 L  · 273 K) / (760 mm Hg  · 298 K)V2 1.796 L Report the result using the correct number of significant figures: V2   1.80 L Applications The combined gas law has practical applications when dealing with gases at ordinary temperatures and pressures. Like other gas laws based on ideal behavior, it becomes less accurate at high temperatures and pressures. The law is used in thermodynamics and fluid mechanics. For example, it can be used to calculate pressure, volume, or temperature for the gas in clouds to forecast weather.