The temperature, T The temperature has to be in kelvin. Don't forget to add 273 if you are given a temperature in degrees Celsius. Using the ideal gas equation Calculations using the ideal gas equation are included in my calculations book (see the link at the very bottom of the page), and I can't repeat them here. There are, however, a couple of calculations that I haven't done in the book which give a reasonable idea of how the ideal gas equation works. The molar volume at stp If you have done simple calculations from equations, you have probably used the molar volume of a gas. 1 mole of any gas occupies 22.4 dm3 at stp (standard temperature and pressure, taken as 0°C and 1 atmosphere pressure). You may also have used a value of 24.0 dm3 at room temperature and pressure (taken as about 20°C and 1 atmosphere). These figures are actually only true for an ideal gas, and we'll have a look at where they come from. We can use the ideal gas equation to calculate the volume of 1 mole of an ideal gas at 0°C and 1 atmosphere pressure. First, we have to get the units right. 0°C is 273 K. T = 273 K 1 atmosphere = 101325 Pa. p = 101325 Pa We know that n = 1, because we are trying to calculate the volume of 1 mole of gas. And, finally, R = 8.31441 J K-1 mol-1. Slotting all of this into the ideal gas equation and then rearranging it gives: And finally, because we are interested in the volume in cubic decimetres, you have to remember to multiply this by 1000 to convert from cubic metres into cubic decimetres. The molar volume of an ideal gas is therefore 22.4 dm3 at stp. And, of course, you could redo this calculation to find the volume of 1 mole of an ideal gas at room temperature and pressure - or any other temperature and pressure. Finding the relative formula mass of a gas from its density This is about as tricky as it gets using the ideal gas equation. The density of ethane is 1.264 g dm-3 at 20°C and 1 atmosphere. Calculate the relative formula mass of ethane. The density value means that 1 dm3 of ethane weighs 1.264 g. Again, before we do anything else, get the awkward units sorted out. A pressure of 1 atmosphere is 101325 Pa. The volume of 1 dm3 has to be converted to cubic metres, by dividing by 1000. We have a volume of 0.001 m3. The temperature is 293 K. Now put all the numbers into the form of the ideal gas equation which lets you work with masses, and rearrange it to work out the mass of 1 mole. The mass of 1 mole of anything is simply the relative formula mass in grams. So the relative formula mass of ethane is 30.4, to 3 sig figs. Now, if you add up the relative formula mass of ethane, C2H6 using accurate values of relative atomic masses, you get an answer of 30.07 to 4 significant figures. Which is different from our answer - so what's wrong? There are two possibilities.
If you need to know about real gases, now is a good time to read about them. © Jim Clark 2010 (last modified July 2017) PV = nRT V = volume (c) Temperature is in kelvin (K) (c) Temperature is in kelvin (K)
Please do not block ads on this website. Deriving the Ideal Gas EquationFor a constant amount of gas:
But what if we do not have a constant amount of gas? What if we were to add more gas, or, remove some gas? What would happen to the volume of the gas then? Avogadro's Principle tells us that, for a gas at constant temperature and pressure, the volume of gas (V) is directly proportional to the number of gas molecules (N): V ∝ N and since a mole is equivalent to Avogadro's Number of molecules, we can say that the volume of a gas (V) is directly proportional to the moles of gas (n) V ∝ n Remember that we combined Boyle's law and Charles' Law to give the Combined Gas Equation: So now we can also include V ∝ n to give a new relationship between the amount of gas (n), its volume (V), pressure (P), and temperature (T): We can turn this relationship into an equation by using a constant of proportionality, R: If we rearrange this equation, we find that If we know the values P, V, n and T then we can find the value of the constant, R. The volume (V) of different amounts of gas (n) was measured at a constant pressure of 101.3 kPa (1 atm) and 298 K (25° C).
If we measure pressure in kilopascals (kPa), volume in litres (L), temperature in Kelvin (K) and the amount of gas in moles (mol), then we find that R = 8.314 and it has the units kPa L K-1 mol-1. The gas constant R is very special because its value does not depend on the nature of the gas used.
So R is called the Gas Constant, and the equation PV = nRT is known as the Ideal Gas Equation, or, as the Ideal Gas Law. Since R depends only on the amount of gas present, and does not depend on what the gas molecules are made up of, then the molecules of gas must not interact with each other, for, if they did, the value of R would be expected to change and reflect the impact of these interactions on the value of pressure (for instance). By rearranging the Ideal Gas Law (Ideal Gas Equation) PV=nRT, it can be used to calculate the pressure (P), volume (V), temperature (T) or amount (n) of gas:
Note that the Ideal Gas Law is supported by the Kinetic Theory of Gases:
Kinetic Theory of Gases tells us that a gas is made up of a huge number of gas particles which are so small that their sizes are negligible compared to the average distances between them, that is, the volume of gas molecules is negligible compared to the volume of space occupied by the gas. V ∝ number of gas molecules So, since the number of gas molecules is related to the amount of gas in moles, the Ideal Gas Law is supported by the Kinetic Theory of Gases.
Do you know this? Join AUS-e-TUTE! Play the game now! Question : What volume is needed to store 0.050 moles of helium gas at 202.6 kPa and 400 K? Solution: (Based on the StoPGoPS approach to problem solving.)
Do you understand this? Join AUS-e-TUTE! Take the test now! Question : What pressure will be exerted by 20.16 g hydrogen gas in a 7.5 L cylinder at 20oC? Solution: (Based on the StoPGoPS approach to problem solving.)
Can you apply this? Join AUS-e-TUTE! Do the drill now! Question : A 50.00 L cylinder is filled with argon gas to a pressure of 10130.0 kPa at 30.00°C. Solution: (Based on the StoPGoPS approach to problem solving.)
Can you apply this? Join AUS-e-TUTE! Take the exam now! Question : To what temperature in Kelvin does a 250.0 mL cylinder containing 0.4000 g helium gas need to be cooled in order for the pressure to be 253.25 kPa? Solution: (Based on the StoPGoPS approach to problem solving.)
Can you apply this? Join AUS-e-TUTE! Take the exam now! |