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Take $\rm NaCl$ for instance, a salt that will melt when it reaches its melting point, and compare it with $\rm NH_4NO_3$, a salt that doesn't melt, but instead decomposes to $\rm N_2O$ and $\rm H_2O$ on heating to a high enough temperature.

How can we determine if a salt will simply melt, or if it will decompose on heating?

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    $\begingroup$ Chemistry is in large extent empirical science. Even if there are various models able to compute various things, for many cases the easiest is just to remember or look up things. An extreme example is melting point of mercury. The about proper value had to be computed by relativistic quantum chemistry and the needed computation power was available just recently. For stability of salts, there may help thermodynamic tables for compounds, but melting points are empirical knowledge. $\endgroup$ – Poutnik Mar 21 '20 at 5:28
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    $\begingroup$ Some info can be semi-derived semi-empirical, based on already learnt behaviour patterns of chemicals, it may be called "chemical sense". But it comes with experience. $\endgroup$ – Poutnik Mar 21 '20 at 6:23
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    $\begingroup$ Long story short, we tell that by knowing chemistry. $\endgroup$ – Ivan Neretin Mar 21 '20 at 6:52
  • $\begingroup$ By heating it up and seeing the results? And if it's explosive ,we'll do it in a fortified chamber. $\endgroup$ – Bruh Moments Jun 5 at 1:36
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As noted, chemistry is an experimental science. That being so, experimental data allow for a few rules. Given that salts are often formed from reactions of acids and bases, we should not be surprised to see acid-base chemistry enter into these considerations.

  1. Salts with three or more elements are more likely to decompose than those that are only binary. Ternary salts often contain within their ions acidic and basic components from which they could form, such as $\ce{CaO + CO2}$ in calcium carbonate or $\ce{MgO + SO3}$ (or, $\ce{MgO + (SO2 + (1/2) O2})$ in magnesium sulfate. In a binary salt such as sodium chloride the original acidic and basic functions have generally been expelled to other compounds, such as water if $\ce{NaCl}$ is formed from $\ce{NaOH + HCl}$.

  2. Within the above criteria, salts are more likely to decompose if the acidic or basic component (such as ammonia among bases) or both are volatile, as entropy becomes more favorable upon heating for the evolution of gases. Silicates (acid = $\ce{SiO2}$) on or in Earth exist under conditions where carbonates (acid = $\ce{CO2}$) would decompose.

  3. Salts with stronger acid and base components are more difficult to decompose, because more energy is required to reverse the acid-base combination. Magnesium sulfate has a higher decomposition temperature than zinc sulfate because magnesium oxide is a stronger base than zinc oxide. Similarly, magnesium sulfate requires a much higher temperature to decompose than magnesium carbonate; the latter decomposition requires evolving weakly acidic $\ce{CO2}$ whereas the former would have to evolve strongly acidic $\ce{SO3}$ or couple the acid-base separation with the thermal decomposition of $\ce{SO3}$ to $\ce{SO2 + (1/2) O2}$. Sometimes redox reactions can facilitate decomposition if they convert stronger acids and bases to weaker ones, such as ammonium nitrate being decomposed to water and nitrous oxide rather than ammonia and nitric acid.

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