Here's what I got.
For starters, you know that you're dealing with a thermal decomposition reaction that takes the general form
#"solid " stackrel(color(white)(acolor(red)(Delta)aaa))(->) " solid residue + gas"#
Now, you know that this salt decomposes to give off brown fumes. A well-known gas that matches this description if nitrogen dioxide,
You can thus say that when the salt undergoes thermal decomposition, nitrogen dioxide is given off.
#"solid " stackrel(color(white)(acolor(red)(Delta)aaa))(->) " solid residue" + "NO"_(2(g))# #uarr#
Now, in order for the reaction to produce nitrogen dioxide, the white salt must contain the nitrate anion,
So all you have to do now is look for an element that has
- a white salt when combined with the nitrate anion
- a yellow oxide
A suitable candidate here is lead,
and lead(II) oxide is a yellow salt
which means that you're dealing with the thermal decomposition of lead(II) nitrate, which produces lead(II) oxide, a yellow solid residue, and brown fumes of nitrogen dioxide. Also, keep in mind that in addition to the nitrogen dioxide, this reaction also produces oxygen gas,
The balanced chemical equation that describes the reaction looks like this
#2"Pb"("NO"_ 3)_ (2(s)) stackrel(color(white)(acolor(red)(Delta)aaa))(->) 2"PbO"_ ((s)) + 4"NO"_ (2(g))# #uarr + "O"_ (2(g))uarr#