You have a 1 L container of a gas at 20°C and 1 atm. Without opening the container, how could you tell whether the gas is chlorine or fluorine?

Question

Owen Ambrose · Accepted Answer

The ideal gas equation is #pV=nRT#, where:
- #p# = pressure, #1atm~~100000Pa#
- #V# = volume, #1L=0.001m^3#
- #T# = temperature, #20^circC~~293K#
- #R# = gas constant.
- #n# = number of moles #n=(pV)/(RT)=(100000*0.001)/(8.31*293)=0.0410706292mol# Asuming the mass of the container is negligible, #n=m/M#, where:
- #m# = mass (#g#)
- #M# = molar mass (#g# #mol^(-1)#) #m=nM#, is you know the mass of the container+gass, and substitute it in, you will get a value for molar mass, and therefore find the gas.h

Owen Ambrose · Answer

Determine the mass of the container plus gas.

This assumes that you know the mass of the container. We can use the Ideal Gas Law to calculate the mass of the gas. #color(blue)(bar(ul(|color(white)(a/a)pV = nRT = m/MRTcolor(white)(a/a)|)))" "# #m = (pVM)/(RT)# If the gas is chlorine, #m = (1 color(red)(cancel(color(black)("atm"))) × 1 color(red)(cancel(color(black)("L"))) × 70.91 "g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1""mol"^"-1"))) × 293.15 color(red)(cancel(color(black)("K")))) = "2.9 g"# If the gas is fluorine, #m = (1 color(red)(cancel(color(black)("atm"))) × 1 color(red)(cancel(color(black)("L"))) × 38.00 "g"·color(red)(cancel(color(black)("mol"^"-1"))))/("0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1""mol"^"-1"))) × 293.15 color(red)(cancel(color(black)("K")))) = "1.6 g"# Thus, if the mass of container plus gas is 2.9 g more than the mass of the empty container, the gas is chlorine. If the mass difference is only 1.6 g, the gas is fluorine.

Caleb Adams · Answer

undefined You could use the ideal gas law to calculate the number of moles of gas in the container and then use the molar mass of chlorine and fluorine to determine which gas is present based on their densities. Chlorine gas has a molar mass of approximately 70.9 g/mol and a density of approximately 3.2 g/L at room temperature and pressure, while fluorine gas has a molar mass of approximately 38.0 g/mol and a density of approximately 1.7 g/L under the same conditions. Comparing the calculated density of the gas in the container with the known densities of chlorine and fluorine gases would allow you to determine the identity of the gas.