10 moles of CH4 at R.T.P would produce what volume of CO2?

Options:
a) 2.4e5 dm3 b) 2.4e2 dm3 c)2.4e4 dm3 d) 2.4e6 dm3

1 Answer
Fleur
Feb 4, 2018

#2.4 xx 10^2 color(white)i "dm"^3 color(white)i "CO"_2#

Explanation:

This problem involves the combustion of methane. In a combustion reaction, oxygen is added to a hydrocarbon to produce carbon dioxide and water.

Here's the unbalanced equation:

#CH_4 + O_2 -> CO_2 + H_2O#

And here's the balanced equation:

#CH_4 + 2O_2 -> CO_2 + 2H_2O#

Since #"1 mol"# #CH_4# produces #"1 mol"# #CO_2#, we know that #"10 mol"# #CH_4# will produce #"10 mol"# #CO_2#.

To find the volume of #CO_2# produced, we can use the Ideal Gas Law, #PV = nRT#, where

  • #P# is the pressure in #"atm"#
  • #V# is the volume in #"L"#
  • #n# is the number of moles
  • #R# is the universal gas constant, #("0.0821 atm" * "L") / ("mol" * "K")#
  • #T# is the temperature in #"K"#

At RTP, room temperature and pressure, the pressure is #"1 atm"# and the temperature is #25^@C#, which is equivalent to #25 + 273 = "298 K"#.

Substitute all of the known values into the equation.

#PV = nRT#

#"1 atm" * V = "10 mol" * ("0.0821 atm" * "L") / ("mol" * "K") * "298 K"#

#V = ("10" cancel "mol" * ("0.0821" cancel "atm" * "L") / (cancel "mol" * cancel "K") * "298" cancel "K")/ ("1" cancel "atm")#

#V = "240 L"#

A total volume of #"240 L"# will be produced; however, the answers are all in units of #"dm"^3#. Since #"1 L" = "1 dm"^3#, the volume is #"240 dm"^3#, or #2.4 xx 10^2 color(white)i "dm"^3#.

Thus, the answer is #"B"#.

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