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How can we prepare magnesium chloride salt using $MgS{{O}_{4}},\text{ }N{{a}_{2}}C{{O}_{3}},\text{ }HCl$?

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Hint:To solve this question, we need to recall different types of reactions, especially double displacement reactions. Firstly, we will undergo a double displacement reaction between magnesium sulfate and sodium carbonate. Now, if we pass HCl through the precipitate formed we will get salt of magnesium chloride.

Complete step-by-step answer:Firstly, we will perform the double decomposition reaction between
$MgS{{O}_{4}}\And \text{ }N{{a}_{2}}C{{O}_{3}}$
We know that in double decomposition reaction, a highly reactive metal displaces less reactive metal from its salt solution.
To know which metal has higher reactivity than the other, we will make use of the reactivity series.
The reactivity of metals in decreasing order is given by the following trend.
$K>Na>Ca>Mg>Al>C>Zn>Fe>Sn>Pb>H>Cu>Ag>Au$
From the above trend we can clearly see that Sodium (Na) is more reactive as compared to magnesium (Mg). So, sodium will displace magnesium from its salt solution.
The reaction is represented as follows;
$MgS{{O}_{4}}\left( aq \right)+N{{a}_{2}}C{{O}_{3}}\left( aq \right)\to MgC{{O}_{3}}\left( s \right)\downarrow +N{{a}_{2}}S{{O}_{4}}\left( aq \right)$
Magnesium carbonate thus formed is insoluble in water and thus it is obtained as precipitate in the solution. Thus, this reaction is an example of precipitation reaction also along with double displacement reaction.
 We will filter the solution using filter paper and will obtain the precipitate.
Now the precipitate thus formed when treated with aqueous solution of Hydrochloric acid yields salt of magnesium chloride. the reaction is represented below;
$MgC{{O}_{3}}\left( s \right)+2HCl\left( aq \right)\to MgC{{l}_{2}}\left( aq \right)+C{{O}_{2}}\left( g \right)\uparrow +{{H}_{2}}O\left( l \right)$
Thus finally, we obtained the magnesium chloride salt.

Note:Magnesium chloride is an essential ingredient of various commercial products. For example, cement, textile and papers. It is also used as a dietary supplement. Magnesium chloride is an ionic salt and thus is highly soluble in water. We can extract the hydrated magnesium chloride from the sea water or brine solution.