6)
Table sugar can be separated from a mixture of
table sugar and sand at STP by adding
(1) sand, stirring, and distilling at 100.°C
(2) sand, stirring, and filtering
(3) water, stirring, and distilling at 100.00
(4) water, stirring, and filtering

Table sugar can be separated from a mixture of  table sugar and sand at STP by adding water, stirring, and filtering.

Table sugar is soluble in water but sand does not dissolve in water. This means that, when i add water to the mixture, the sugar dissolves.

The dissolved sugar is collected as part of the filtrate while the sand remains as the residue.

If I desire to collect the pure sugar, I can evaporate the filtrate to dryness.

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(4) Water, stirring, and filtering  

Explanation:

The added water will dissolve the sugar but not the sand. When you filter the mixture, the sand will be trapped in the filter paper and the dissolved sugar will pass through the pores of the paper.

(1) and (2) are wrong. You don't separate a mixture of sugar and sand by adding more sand. Furthermore, neither substance will boil at 100 °C.

(3) is wrong. You can dissolve the sugar in water but, if you boil the water away, the sugar and sand will still be together.

the product of the pressure and volume is also constant