During a chemical reaction, equal moles of two diatomic molecules X and Y are al

Question

During a chemical reaction, equal moles of two diatomic molecules X and Y are allowed to react to form one gaseous compound XnYm. After the reaction is complete, it was observed that the density of the product formed is 1.50 greater than the density of the reactant mixture.

a. Specify the formula of the product, XnYm
b. Is more than one answer possible based on given information?
c. Would you say that the formula you found in (a) is empirical or molecular formula?

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Explanation / Answer

X2 + Y2 ---> XnYm + excess reactant

there are several uncertainties that arise from the wording of the equation. First does one mol X react with 1 mol Y? We must assume not necessarily. This then gives us a problem about what is meant by product. Normally that would mean just the XnYm, but that can't be quite correct here as you would then not have enough information to find a result. My guess here is that product means XnYm plus the excess reactant, just as density of reactant means density of the mixture of X and Y.

So you start with 2 moles gas with a particular volume V and density where d = m/V and Avogadro's law says V is proportional to number of moles (n)

At the end the new density is 1.50 times as much. The total mass m has not changed so the new volume must be 1/1.5 = 0.667 times. Where the fraction of volume change is the same fraction of a change in the moles present. In other words the total number of moles of gass at the end is 2 x 0.667 = 1.33 for a decrease in 2 - 1.33 = 0.665 mol of gas

So 1 mol of the limiting reactant must have combined with 0.667 mol of the excess reactant to give one mol of XnYm and leaving 0.333 mol of the excess reactant

We don't know which is the limiting reactant so there are two possible answers. I will work the one for X2 as limiting reactant (there is another solution for Y2 as the limiting reactant) So the equation is

X2 + 0.667Y2 = XnYm

giving n = 2 and m = 1.333

multiply by 3 to give the simplest whole number ratio give n = 6 and m = 4

so X6Y4

This is an empirical formula and the other possible formula would be X4Y6

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