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$$\mathrm{molarity} = \frac{\text{amount of solute}}{\text{volume of solution}} $$ and amount of substance is based on quantity (larger mass means larger amount), so how come it is an intensive property. Shouldn't it be an extensive property?

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    $\begingroup$ Very firstly, no. of moles doesn't depend on weight, it depends on mass. If you will take 12g of Carbon to the moon, it will have same no. of moles on moon as on earth. $\endgroup$ – ashu Oct 16 '13 at 10:33
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Concentration is an intensive property. The value of the property does not change with scale. Let me give you an example:

Let us say you had a homogenous mixture (solution) of sodium carbonate in water prepared from 112 g of sodium carbonate dissolved in 1031 g of water.

The concentration (in mass percent, or mass of solute per mass of solution) is:

$$c=\frac{112\text{ g solute}}{(112+1031)\text{g solution}}=0.09799 =9.799\%\text{ sodium carbonate by mass}$$

The concentration is the ratio of sodium carbonate to the total mass of the solution, which does not change if you are dealing with the entire 1143 g of the solution or if you dispense some of that solution into another vessel.

If you dispense 11.7 g of that solution into a flask for a reaction, what is the concentration of sodium carbonate in that flask?

It is still 9.799% by mass. The ratio of the mass of sodium carbonate present to the total mass present has not changed. The actual mass of sodium carbonate has changed:

$$0.09799\dfrac{\text{g solute}}{\text{g solution}}\times11.7\text{ g solution}=1.15\text{ g solute}$$

The concentration is a property dependent only on the concentration of the solution, not the amount of solution you have. The concentration of a solution with defined composition is independent of the size of the system.

In general, any property that is a ratio of two extensive properties becomes an intensive property, since both extensive properties will scale similarly with increasing or decreasing size of the system.

Some examples include:

  • Concentration (including molarity) - ratio of amount of solute (mass, volume, or moles) to amount of solution (mass or volume usually)
  • Density - ratio of mass of a sample to the volume of the sample
  • Specific heat - ratio of heat transferred to a sample to the amount of the sample (mass or moles usually, but volume also)

Each of these intensive properties is a ratio of an extensive property we care about (amount of solute, mass of sample, heat transferred) divided by the scale of the system (amount of stuff usually). This is like finding the slope of a graph showing the relationship between two extensive properties. The graph is linear and the value of slope does not change based on how much stuff you have - thus the slope (the ratio) is an intensive property.

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Consider the following picture:
enter image description here

Break the ice block shown in the picture into two equal halves.Now I hope you would be able to answer the following questions:
1.What are the physical properties of ice block which got halved?
Absolutely mass,volume,etc.(These are all extensive properties.)
2.What are the physical properties of ice block which remained same?
Density,etc.(These are all intensive property.)
If you have the doubt so as to why the density remained same,here is the explanation:
I hope you know basically even if block got halved,mass per unit volume remains the same in either of the pieces.All the way it mean that density remained the same(mass per unit volume).Thus it is an intensive property.
Similarly if you imagine solution instead of ice block,you will find that molarity remains the same even if you divide solution into two equal halves.Thus molarity is a intensive property.

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