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A water insoluble substance ‘X’ on reacting with dilute ${H_2}S{O_4}$ released a colourless odourless gas accompanied by brisk effervescence. When the gas was passed through water, the solution obtained turned blue litmus red. On bubbling the gas through lime water, it initially became milky and the milkiness disappeared when the gas was passed in excess. Identify the substance ‘X’ and write the chemical equations involved.

Answer
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Hint: Limewater is the general name for a dilute aqueous solution of calcium hydroxide whose chemical formula is $Ca{(OH)_2}$. It is a clear and colourless liquid with a bitter taste and it is sparingly soluble in water. It is the most common method to be used for the specific test of carbon dioxide as it turns into a cloudy white solution when $C{O_2}$ is passed through the solution.

Complete answer: As per question, gas X reacts with a dilute solution of sulphuric acid to give brisk effervescence which indicates that the carbon dioxide gas is evolved in the reaction. The equation for the chemical reaction can be written as follows:
$X + {\text{dil}} \cdot {H_2}S{O_4} \to Y + C{O_2} + {H_2}O$
As carbon dioxide is produced as a product that means the reactant must consist of a carbon atom and it is given that X is water insoluble substance, so it must be calcium carbonate which is insoluble in water and on reaction with dilute sulphuric acid gives a colourless gas of calcium sulphate. Therefore, the reaction involved in the process is as follows:
 $CaC{O_3} + {\text{dil}} \cdot {H_2}S{O_4} \to CaS{O_4} + C{O_2} + {H_2}O$
In the next step, it is given that the gas i.e., carbon dioxide was passed through water due to which formation of carbonic acid takes place. As acid is formed in the product, so it changes blue litmus into red. The reaction involved in the process is as follows:
$C{O_2} + {H_2}O \to {H_2}C{O_3}$
Now, on passing carbon dioxide gas to lime water, formation of calcium carbonate takes place which has a cloudy white appearance. The reaction is as follows:
$Ca{(OH)_2} + C{O_2} \to CaC{O_3}(s)$
When the gas is passed in excess, the calcium carbonate reacts with $C{O_2}$ to form calcium bicarbonate which is a colourless solution. Hence, milkiness disappears when carbon dioxide reacts with lime water in excess. The reaction is as follows:
$CaC{O_3} + C{O_2} \to CaHC{O_3}(aq)$
Therefore, the substance ‘X’ considered is calcium carbonate with a chemical formula $CaC{O_3}$.

Note:
It is important to note that different gases are identified by their unique observation made when the removal of the gas takes place during any chemical reaction. Some common observations are brisk effervescence which means rapid evolution of a gas during a chemical reaction. It is evidence for liberation of carbon dioxide gas in a chemical reaction, evolution of a gas with a pop sound proves the liberation of hydrogen gas, etc.