Answer:
Dr Haruhiko Yokoyama kindly answered the above question.
    
   
There are two kinds of decreasing volume: 

1. The volume becomes less than the volume of water, when a substance is added to water.
      

2. The volume becomes less than the total volume (total volume of water and substance), when a substance is added to water.  

Many substances illustrate case 2.  Sodium chloride and ethanol, for example. However, since I think that this questioner is asking about case 1, I will describe this reason.
   
The reason why the volume is decreased
For example, it is well known that the volume is decreased when magnesium sulfate is added to a lot of water.  The reason is that the structure of water, which has many spaces because of hydrogen bonds, changes to become more closely packed around the metal ion (hydration), when metal ion is added into water.  In the case of magnesium ion, the number of water molecules which directly hydrate (the number of water molecules in first hydration shell) is 6, and all 6 water molecules interact with the magnesium ion, attracting the oxygen atom of water molecules to it.  Also, there are 12 water molecules (water molecules in second hydration shell) outside the first hydration shell, and there are hydrogen bonds between the water molecules in the first and second hydration shells.  As a result, the water molecules around metal ions are denser than water molecules in pure water.  This is the reason why the volume is decreased when metal ion is added to water.
  
Although the volume of the solution increases by the volume of the metal ion itself, the total volume of the magnesium ion solution decreases because the volume of metal ion is usually small, and the effect of decreasing volume by hydration is high (in case of magnesium ion, etc).  Sulfate ion is different from metal ion.  The volume of sulfate ion itself is big, causing an effect is larger than the effect of hydration.  So the volume of solution increases when sulfate ion is added.  In fact, the effect of magnesium ion (decreased volume) is larger than the effect of sulfate ion (increased volume).  So the volume of the solution decreases when magnesium sulfate is added to water. 
   
In the case of sodium ion, its volume is a bit smaller than magnesium ion, and hydration is relatively weaker because it is not divalent but monovalent.  Although there is an effect of decreasing volume when sodium ion enters water, its effect is smaller than for magnesium ion.  Thus, when sodium chloride is dissolved to water, the volume does not decrease because the effect of increasing the volume caused by the chloride ion is larger than that of decreasing the volume by the sodium ion. However, in the case of sodium hydroxide, the volume of hydroxide ion is small, and the hydration is stronger than that of the chloride ion.  So the volume of the solution is decreased when sodium hydroxide is dissolved in water.
  
Substances which decrease/increase the volume of solution
This measurement shows how anion/cation (per mol) are affected by changing volume, by observing how the water solution changes when a slight amount of electrolyte is added to it.  If the value is negative, the ion decreases the volume of solution.  If it is positive, the ion increases the volume.  These are typical examples:
   

   
Let me explain how to calculate the volume change using this table when an electrolyte is dissolved in water.  In the case of MgSO₄, for example, -32.0 + 24.8 = -7.2 cm³ (per mol). However, we can use this table only when the concentration is very low.  For example, when the concentration of MgSO₄ is 0.0001 mol/L, the 1 L of water decreases the volume approximately -7.2 x 0.0001 = -0.00072 cm³.  As the concentration increases, the number of water molecules for hydration decreases and the hydration weakens because the distance between cation and anion becomes less.  Thus, when the concentration is 1 mol, the decrease of the volume is not – 7.2 cm³ but a much smaller value.
 
In case of sodium hydroxide, the volume also decreases, i.e., -6.6 + 1.4 = -5.2 cm³/mol.  Like the case of magnesium sulfate, the effect of decreasing volume goes down as the concentration increases.
  
As for sodium chloride, -6.6 + 23.2 = +16.6, therefore, the volume increases when it is added to water.  However, since the volume of the sodium chloride crystal is 27 cm³/mol, the volume of sodium chloride solution is smaller than the sum of the volume of water and sodium chloride.
  
Note: Magnesium sulfate in this article always represents magnesium sulfate anhydrous.  Ordinary magnesium sulfate is hydrated 6 or 7.  If the hydrated magnesium sulfate is dissolved in water, the volume of solution does not decrease because of the hydrated water.
  
  
Acknowledgement
Our thanks to Dr. Haruhiko Yokoyama
He is studying the solution structure and ion solvation.
  
 

*This article is translated by Chemistryquestion.com from the original article in Chemistryquestion.jp.  Please let us know if you find any errors.