What mass of 10°c water will dissolve 350 g of potassium chloride to form a saturated solution?

Solubility of KCl in 70C water is about 47 g/100g water. Thus in 250 grams of water, you should be able to dissolve about 117.5 grams KCl.

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Alt. Source: //www.kentchemistry.com/links/Kinetics/SolubilityCurves.htm

If you want to know the maximum mass of KCl that will dissolve in water at 70°C, you need to know the solubility of KCl in water at that temperature. Let's suppose that X g of KCl can dissolve in 1 kg of water at 70°C, then the number of grams of KCl that can dissolve in 250 g water at 70°C is given by:

X gm KCl / 1 Kg H2O • 1Kg H2O/1000g H2O • 250 g H2O

the units gm H2O and Kg H2O cancel, and you are left with gm KCl.