Coal gasification is a process that converts coal into methane gas. If this reaction has a percent yield of 85.0%, how much methane can be obtained from 1250 g of carbon?
1 Answer
Explanation:
Start by writing the balanced chemical equation that describes this reaction
#color(blue)(2)"C"_ ((s)) + 2"H"_ 2"O"_ ((g)) -> "CO"_ (2(g)) + "CH"_ (4(g))#
Notice that the reaction produces
This represents the reaction's theoretical yield, i.e. what you get if the reaction has a
You can convert this mole ratio to a gram ratio by using the molar masses of carbon and methane
#2 color(red)(cancel(color(black)("moles C"))) * "12.011 g"/(1color(red)(cancel(color(black)("mole C")))) = "24.022 g"#
#1 color(red)(cancel(color(black)("mole CH"_4))) * "16.04 g"/(1color(red)(cancel(color(black)("mole CH"_4)))) = "16.04 g"#
You can thus say that the theoretical yield of the reaction will have it produce
This means that
#1250 color(red)(cancel(color(black)("g C"))) * "16.04 g CH"_4/(24.022color(red)(cancel(color(black)("g C")))) = "834.65 g CH"_4#
Now, the reaction is said to have an
As a result, the actual yield of the reaction will be
#834.65 color(red)(cancel(color(black)("g CH"_4))) * "85.0 g produced"/(100color(red)(cancel(color(black)("g CH"_4)))) = color(darkgreen)(ul(color(black)("709 g CH"_4)))#
The answer is rounded to three sig figs.