Question #265c0

1 Answer
Aug 22, 2017

Answer:

Here's how you can do that.

Explanation:

Your starting point here will be the ideal gas law equation, which looks like this

#color(blue)(ul(color(black)(PV = nRT)))#

Here

  • #P# is the pressure of the gas
  • #V# is the volume it occupies
  • #n# is the number of moles of gas present in the sample
  • #R# is the universal gas constant, equal to #0.0821("atm L")/("mol K")#
  • #T# is the absolute temperature of the gas

Now, let's say that the given mass of gas is #m#. The number of moles of gas present in this given mass #m# depends on the molar mass of the gas, let's say #M_M#.

#n = m /M_M#

Plug this into the ideal gas law equation to get

#PV = m/M_M * RT#

Next, divide both sides of the equation by #T# to get

#(PV)/T = m/M_M * R#

The molar mass of the gas, which tells you the mass of exactly #1# mole of the gas, is constant.

#(PV)/T = overbrace(R/M_M)^(color(blue)("constant")) * m#

#(PV)/T = color(blue)("constant") * m#

This means that for a given mass #m#, i.e. if you use a sample of gas of constant mass, you can say that

#(PV)/T = color(blue)("constant")#

This is the combined gas law equation and it tells you that for a given mass of gas #m#, you have

#color(blue)(ul(color(black)((P_1V_1)/T_1 = (P_2V_2)/T_2)))#

Here

  • #P_1#, #V_1#, #T_1# are the pressure, volume, and absolute temperature of the gas at an initial state
  • #P_2#, #V_2#, #T_2# are the pressure, volume, and absolute temperature of the gas at a final state

http://study.com/academy/lesson/combined-gas-law-definition-formula-example.html