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The burning of Magnesium in air results in the formation of Magnesium Oxide and:
$\begin{align}
 & a)M{{g}_{3}}{{N}_{2}} \\
 & b)MgC{{O}_{3}} \\
 & c)Mg{{(N{{O}_{3}})}_{2}} \\
 & d)Mg{{(N{{O}_{2}})}_{2}} \\
\end{align}$

Answer
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Hint: The two major constituent gases of the air are Nitrogen and Oxygen. Therefore, the burning of Magnesium in air should result in the production of compounds obtained when it reacts with these two gases.

Complete step by step solution:
Having seen the hint as given above, let us now look at the reaction between Magnesium and Oxygen. This can also be characterised as a combustion reaction, as it gives off heat and light. The reaction is as follows:

$2Mg(s)+{{O}_{2}}(g)\xrightarrow{\Delta }2MgO(s)$

The product of this reaction is magnesium oxide and its molecular formula is $MgO$.
However, since this product is already accounted for, our answer is most certainly the product obtained from the burning of Magnesium in Nitrogen.
Now that we have established exactly what we are looking for, let us now observe this reaction of Magnesium and Nitrogen.

$3Mg(s)+{{N}_{2}}(g)\xrightarrow{\Delta }M{{g}_{3}}{{N}_{2}}(s)$

As shown above, the reaction yields Magnesium Nitride. Therefore, the answer to this question is option (a) $M{{g}_{3}}{{N}_{2}}$.
The other compounds given in the options are not possible because the atmospheric combustion of any substance is simply a reaction with oxygen. Magnesium nitride formed in this case is so because of the abundance of nitrogen gas. In the atmosphere, substances like carbonates, nitrates and nitrites are not found in concentrations that could intervene in any reaction happening in the surrounding.

Note: The reaction equations written above should always be balanced. An unbalanced equation always leaves out many crucial details. The equation should also contain the states of the reactants and products. Thus making it a complete equation.