Combined gas law and ideal gas law


Created with CAST's UDL Book Builder

Combined gas law

  • This law combines the three major gas laws:
  • The equation is:    P1 x V1   =  P2 x V2
  •                                  T1               T2
  • The other laws can be obtained from this law by holding one quantity (pressure, volume, or temperature) constant.
  • This law also allows you to make calculations when none of the variables are held constant.
Created with CAST's UDL Book Builder

Ex 1)

  • if you hold temperature constant (T1 = T2), rearrange the combined gas law to get the two temperature terms on the same side of the equation and then cancel. 
  • P1 x V1 = P2  x  V2  because the temperature cancel out.
Created with CAST's UDL Book Builder

Ex 2)

  • The volume of a gas filled balloon is 30.0 L at 40oC and 153 kPa. What volume will the balloon have at standard temperature and pressure (STP which is 101.3 kPa and 273 K)?
  • Start with the knowns:
  • V1 = 30.0 L
  • T1 = 40oC + 273 = 313 K
  • P1 = 153 kPa
  • T2 = 273 K
  • P2 = 101.3 kPa
  • Unknown:
  • V2 = ? L
  • Rearrange the formula to get V2 by itself
  • V2 =  V1 x P1 x T2
  •             P2 x T1
  • Substitute the knowns into the equation and solve:
  • V2 = 30.0 L x 153 kPa x 273 K =
  •              101.3 kPa x 313K
  • 39.5 L
Created with CAST's UDL Book Builder

Ideal Gas Constant

  • Until now we have ignored the amount of gas, this is where the ideal gas law comes in
  • Knowing that 1 mol of any gas occupies 22.4 L at STP(101.3 kPa and 273 K) gives you the following value
  • R = P x V =  101.3 kPa x 22.4 L = 8.31
  •       T x n       273 K x 1 mol
  • The Units would be (kPa x L)/(K x mol)
  • This is the ideal gas constant (R)
Created with CAST's UDL Book Builder

The ideal gas law

  • The ideal gas law is P x V = n x R x T
  • The reason to use the ideal gas law rather than the combined gas law is it allows you to take into account the number of moles of a gas.
Created with CAST's UDL Book Builder

Ex)

  • You fill a rigid steel cylinder that has a volume of 20.0 L with nitrogen gas (N2) (g) to a final pressure of 2.00 x 104 kPa at 28oC. How many moles of N2 (g) does the cylinder contain?
  • First list the knowns:
  • P = 2.00 x 104 kPa
  • V = 20.0 L
  • T = 28oC + 273 = 301 K
  • R = 8.31 (kPa x L) / (K x mol) 
  • Unknown:
  • n = ? mol N2(g) 
  • rearrange the equation to get the unknown by itself 
  • n =  P x V  
  •        R x T
  • Substitute the knowns: 
  • n =  2.00 x 104kPa x 20.0 L x K x mol
  •        8.31 L x kPa x 301 K
  • n =160 mol N2 (g)
Created with CAST's UDL Book Builder

complete the student response section

Created with CAST's UDL Book Builder