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### Topic: stoichiometry: Find formula of compound X.  (Read 6973 times)

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#### carlsone

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##### stoichiometry: Find formula of compound X.
« on: December 29, 2013, 02:12:48 AM »
0.144 g of an aluminium compound X react with an excess of water, to produce a gas. This gas burns completely in O2 to form H2O and 72 cm3 of CO2 only. The volume of CO2 was measured at room temperature and pressure.
What could be the formula of X?

[C = 12.0, Al = 27.0; 1 mole of any gas occupies 24 dm3 at room temperature and pressure]

A Al2C3  B Al 3C4  C Al 4C3  D Al 5C3

The 72cm3 is equivalent to 0.003 moles of Carbon. This is equal to 0.003 x 12 = 0.036g of Carbon. Subtracting from 0.144 g of the compound gives 0.108g of Aluminium or 0.108/27=0.004 moles. The ratio of the two moles gives C as the ans. I am not comfortable with this though,any more logically approaches.

There's another approach posted here:http://sgforums.com/forums/2297/topics/443584 but I am not following how the ratio of 4/3 was obtained, the expression is difficult to follow. Any help would be much appreciate for this first post .

#### Borek

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##### Re: stoichiometry: Find formula of compound X.
« Reply #1 on: December 29, 2013, 04:00:14 AM »
The 72cm3 is equivalent to 0.003 moles of Carbon. This is equal to 0.003 x 12 = 0.036g of Carbon. Subtracting from 0.144 g of the compound gives 0.108g of Aluminium or 0.108/27=0.004 moles. The ratio of the two moles gives C as the ans. I am not comfortable with this though,any more logically approaches.

That's a perfectly correct approach, IMHO thebest one - you perfectly ignore everything that is irrelevant.

Quote
There's another approach posted here:http://sgforums.com/forums/2297/topics/443584 but I am not following how the ratio of 4/3 was obtained, the expression is difficult to follow. Any help would be much appreciate for this first post .

As you have correctly noticed, the approach presented there (while correct) is much more difficult to follow, which makes your answer better.

Basically they derived the equation

$$3\times 10^{-3} = y \frac {0.144}{27x + 12y}$$

If you multiply both sides by 27x+12y, then group all terms containing x an one side of the equation and those containing y on the other side, you will get something like

$$ax=by$$

which is equivalent to

$$\frac x y = \frac b a$$
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#### carlsone

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##### Re: stoichiometry: Find formula of compound X.
« Reply #2 on: December 29, 2013, 07:31:25 AM »
This is appreciated thanks, it's good to have the alternative approach sorted out as well.