Multiple choice

What is the quantity of water that should be added to $16$ g methanol to make the mole fraction of methanol as $0.25$?

  1. 27 gm

  2. 12 gm

  3. 18 gm

  4. 36 gm
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A Correct answer
Explanation

Mole fraction of methanol = moles methanol / (moles methanol + moles water). Moles methanol = 16/32 = 0.5. 0.25 = 0.5 / (0.5 + n_water). 0.5 + n_water = 2. n_water = 1.5 moles. Mass of water = 1.5 * 18 = 27g.

AI explanation

The molar mass of methanol (CH3OH) is 32 g/mol, so 16 g is 0.5 moles. If the mole fraction of methanol is 0.25, then its moles make up one-fourth of the total moles in the mixture, meaning the other three-fourths must be water. Therefore, water must constitute 1.5 moles (because 0.5 is one-fourth of 2). The molar mass of water is 18 g/mol, so the required mass is 1.5 moles times 18 g/mol, which is 27 g.

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