Question #b629a

1 Answer
May 22, 2017

Answer:

#"4.3M g mol"^(-1)#

Explanation:

For starters, it's worth mentioning that NTP conditions are defined as a pressure of #color(blue)(ul(color(black)("1 atm")))# and a temperature of

#color(blue)(ul(color(black)(20^@"C"))) = 20^@"C" + 273.15 = color(blue)(ul(color(black)("293.15 K")))#

Now, use the ideal gas law equation to calculate the molar volume of the gas at NTP, i.e. the volume occupied by #1# mole of any ideal gas under NTP conditions.

#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

Rearrange the equation

#V/n = (RT)/P#

Plug in your values to find

#V/n = (0.082 (color(red)(cancel(color(black)("atm"))) * "L")/("mol" * color(red)(cancel(color(black)("K")))) * 293.15 color(red)(cancel(color(black)("K"))))/(1color(red)(cancel(color(black)("atm"))))#

#V/n = "24.04 L mol"^(-1)#

This tells you that #1# mole of any ideal gas occupies #"24.04 L"# under NTP conditions.

You can thus say that your sample, which is said to occupy #"5.6 L"# under these conditions, will contain

#5.6 color(red)(cancel(color(black)("L"))) * "1 mole"/(24.04color(red)(cancel(color(black)("L")))) = "0.2329 moles"#

As you know, the molar mass of a substance is defined as the mass of exactly #1# mole of said substance.

In your case, #1# mole of this substance will have a mass of

#1 color(red)(cancel(color(black)("mole"))) * "M g"/(0.2329 color(red)(cancel(color(black)("moles")))) = (1/0.2329 * "M")# #"g"#

Therefore, you can say that the molar mass of the substance is equal to

#color(darkgreen)(ul(color(black)("molar mass" = (4.3 * "M")color(white)(.)"g mol"^(-1))))#

The answer is rounded to two sig figs, the number of sig figs you have for the volume of the sample.