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Why does dry $HCl$ gas not change the colour of the dry litmus paper?

Answer
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Hint: The litmus paper is used to determine the acidic or basic nature of a solution based on color change of litmus paper. The reason behind the colour change in litmus paper is due to the presence of hydrogen ions. In dry $HCl$ the ionization wouldn't take place.

Complete step by step answer:
  -As we know the term acid and base have been defined in different ways in chemistry. Generally, we can say that an acid is any hydrogen-containing substance which is capable of donating hydrogen ion(proton) to another substance.
  -Solutions can be classified as acidic or basic on their hydrogen ion concentration relative to pure water. If the pH is below seven, then the solution is acidic and if it is greater than seven the solution is said to be basic.

 - By using a litmus paper, we could easily find whether a solution is acidic or neutral. Hence, we can say that it is a type of acid base indicator
  - The litmus paper is available in blue, red and neutral variations. Depending on the nature of the solution the litmus paper changes its colour on interaction with the solution.
  - The red litmus paper can be used to detect the alkaline pH and this alkalinity will turn the shade to a shade of blue in the presence of a basic solution. Similarly, blue litmus paper can be used to test for acidic nature and will turn the blue shade into a red shade if it comes in contact with a solution of acidic nature. Also, the neutral litmus paper is purple and its colour will change accordingly depending on the nature of the solution which is tested.

  - The reason for blue litmus turning into red is due to the presence of hydrogen ion concentrations. In in the presence of water we can write the dissociation of $HCl$ as follows
$HC{{l}_{(aq)}}\rightleftharpoons \quad H_{(aq)}^{+}+Cl_{(aq)}^{-}$

   - If we are taking dry $HCl$ , there is no ${{H}^{+}}$ ion present in dry $HCl$ gas. This is because in the absence of water , the highly concentrated positive charge of hydrogen ion would rejoin with $C{{l}^{-}}$ ion to get back the lost electron in order to reform the $HCl$ molecule.
  - Since there are no ${{H}^{+}}$ ions ,the dry $HCl$ gas would not be able to change the colour of dry litmus from blue to red.

Note: Another explanation can also be given for this. As we know, water is a polar solvent and hence water has high solvation energy and high value of dielectric constant. When $HCl$ is dissolved in water, ionization takes place which leads to the formation of hydrogen and chlorine ions. The hydronium ion is formed by the further hydrogen ions which are hydrated in water. In dry $HCl$ this ionization will not take place and thus no hydrogen ion present in dry $HCl$ gas and thus no action on litmus paper.