Combined and Ideal Gas Laws - Chemistry PDF

Name: Combined and Ideal Gas Laws Notes: Additional Notes: By combining the different gas laws you can create two new gas laws, the Combined Gas Law:...

Name: Combined and Ideal Gas Laws Notes: Additional Notes: By combining the different gas laws you can create two new gas laws, the Combined Gas Law: 𝑃1𝑉1 𝑃2𝑉2 𝑛1𝑇1 = 𝑛2𝑇2 and since: 𝑃1𝑉1 𝑃2𝑉2 𝐿·𝑎𝑡𝑚 𝑛1𝑇1 = 𝑛2𝑇2 = R = 0.08206 𝑚𝑜𝑙·𝐾 = Universal Gas Constant the Ideal Gas Law: 𝑃𝑉 𝑛𝑇 =R or PV = nRT If you use different units for pressure, you must use a different value for R. Pressure Units Value for R atm 0.08206 𝐿·𝑎𝑡𝑚 𝑚𝑜𝑙·𝐾 kPa 8.314 𝐿·𝑘𝑃𝑎 𝑚𝑜𝑙·𝐾 mmHg and torr 62.36 𝐿·𝑚𝑚𝐻𝑔 or 62.36 𝐿·𝑡𝑜𝑟𝑟 𝑚𝑜𝑙·𝐾 𝑚𝑜𝑙·𝐾 The combined gas law is used when there is a change in conditions and the ideal gas is used when there is not a change in the conditions. If you have a change in conditions AND you are not given any information about one of the variables, then you can assume that it is constant and you can cancel that variable out. In any gas law problem, your first step is to determine which formula you will use. Example: A 3.25 L sample of hydrogen gas had a pressure of 2.09 atm when the temperature was 305 K, what will the pressure of this sample be when the volume is 6.90 L and the temperature is 455 K? A Chemistry Guide  How many moles of carbon dioxide are there in a rigid 5.50 L container at 25.0℃ if the pressure is 125 kPa? The ideal gas law can also be used to determine by what factor a gas will change under different conditions. To solve this type of problem, follow these steps: 1) Rewrite the ideal gas law to solve for the variable you are asked about. 2) Plug in the values that change, ignore the variables that don’t change (you can put in a 1). 3) Simplify and solve. For example: By what factor will the pressure of a gas change if the volume is doubled while the temperature in Kelvin is increased by 50%? 𝑛𝑅𝑇 1) PV=nRT ∴ P= 𝑉 2) P= (1)(1)(1.5) = (No change to n)(No change to R)(T increases by 50% so multiply by 1.5) (2) (V is doubled, multiply by 2) 3) P = 1.5 = 0.75, which means that the pressure will be 0.75 times the original pressure value. 2 By what factor will the volume change, if the pressure is halved and the temperature is tripled? I do: Answer: What is the volume of a gas at STP if the gas has a volume of 11.2 L when the pressure is 653 mmHg and the temperature is 98.5℃? A Chemistry Guide  We do: A 0.843 mole sample of a gas at 63.3 ℃ occupies a volume of 18.9 L, what is the pressure of this sample in atm? We do: By what factor will the temperature change if the pressure is doubled and the number of moles is reduced by ⅓? You do: 1) If you have 0.857 moles of gas with a volume of 1.97 L at a pressure of 0.942 atm, what is the temperature of the gas in K? 2) What is the new pressure of 8.00 mL of a gas at 453 K if it occupies 5.00 mL at a pressure of 565 torr and 978 K? A Chemistry Guide  3) How many moles of carbon dioxide are there in a 5.12 L sample at 93.2 ℃ with a pressure of 232 kPa? 4) What volume would 1.00 moles of a gas occupy at 1.00 atm and 298 K? 5) A gas has a volume of 0.652 L at 952 K when the pressure is 951 mmHg, what is the Kelvin temperature when the volume is 0.987 L and the pressure is 637 mmHg? 6) If you have a sample of a gas at 2.09 atm and 387 K, what will the pressure (in atm) be when the temperature is 305 K? 7) By what factor will the volume change if the Kelvin temperature is halved and the pressure is reduced to ¼? 8) What is the temperature (in Celcius) of 0.0974 moles of a gas that has a volume of 3.87 L at a pressure of 2.01 atm? 9) By what factor will the temperature change if the pressure is reduced by ¼ and the volume is increased by ⅓? A Chemistry Guide  10) What is the pressure of 1.58 L of a gas at 25.0℃ if the pressure is 3.21 atm when the volume is 2.64 L and the temperature is 50.0℃? A Chemistry Guide