Question #11cbb
1 Answer
Explanation:
Start by writing a balanced chemical equation that describes the combustion of a hydrocarbon
#"C"_ x"H"_ (y(g)) + (x + y/4)"O"_ (2(g)) -> x"CO"_ (2(g)) + y/2"H"_ 2"O"_((g))#
Your job here will be to determine the value of
The idea here is that when two gases are kept under the same conditions for pressure and temperature, the ratio that exists between their moles is equivalent to the ratio that exists between their volumes.
You can prove this by using the ideal gas law equation, which looks like this
#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "# , where
Now, let's say that the conditions for pressure and temperature are
#P * V_1 = n_1 * RT -># the reactants' side
Likewise, if you take
#P * V_2 = n_2 * RT -># the products' side
Divide these two equations to get
#(color(red)(cancel(color(black)(P))) * V_1)/(color(red)(cancel(color(black)(P))) * V_2) = (n_1 * color(red)(cancel(color(black)(RT))))/(n_2 * color(red)(cancel(color(black)(RT))))#
which gets you
#color(purple)(|bar(ul(color(white)(a/a)color(black)(n_1/n_2 = V_1/V_2)color(white)(a/a)|))) -># the mole ratio is equivalent to the volume ratio
So, the total number of moles present on the reactants' side will be
#n_1 = 1 + (x + y/4)#
This is the case because
The total number of moles present on the products' side will be
#n_2 = x + y/2#
Here,
This means that you have
#(1 + x + y/4)/(x + y/2) = (600 color(red)(cancel(color(black)("mL"))))/(700color(red)(cancel(color(black)("mL"))))#
which is equivalent to
#(1 + x + y/4)/(x + y/2) = 6/7#
At this point, all you have to do is solve this for
#1 + x + y/4 = 6 implies x = 5 - y/4#
You will have
#5 - y/4 + y/2 = 7#
#y/4 = 2 implies y = 8#
The value of
#x = 5 - 8/4 = 3#
Therefore, the molecular formula of this unknown hydrocarbon is
#color(green)(|bar(ul(color(white)(a/a)"C"_3"H"_8color(white)(a/a)|))) -># propane