When heated by a flame, ammonium dichromate decomposes, producing nitrogen gas, solid chromium(III) oxide, and water vapor.
$$\left(\mathrm{NH}_{4}\right) 2 \mathrm{Cr}_{2} \mathrm{O}_{7} \rightarrow \mathrm{N}_{2}+\mathrm{Cr}_{2} \mathrm{O}_{3}+4 \mathrm{H}_{2} \mathrm{O}$$
Write the mole ratios for this reaction that relate ammonium dichromate to the products.