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Well vapor pressure also depends on the mole fraction of a substance.

Vapor pressure= Mole fraction* Total pressure of the solution.

If the Mole fraction of a volatile substance in the solution is decreased its vapor pressure increases. Thus the volatility of the substance barely plays the role. Of course, if the solution has no volatile substance there cannot be any vapor pressure in the container.

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Q: How does a solution containing a chemical with a high vapor pressure be low in volatility?
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