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The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesives, inks, and pharmaceuticals) showed that it contained 40.0 percent C, 6.7 percent H, and 53.3 percent O. A solution of 0.650 g of the solid in 27.8 g of the solvent diphenyl gave a freezing-point depression of . Calculate the molar mass and molecular formula of the solid. ( for diphenyl is .)
The problem asks to determine the molar mass of the unknown solute and to identify its molecular formula using the given empirical formula .
In this example, the required conversions are
Calculate the molality of the solution from the depression in freezing point
From molality, determine the number of moles.
Determine the mass.
We are going to use this approach:
is the depression in the solution's freezing point
is the molal freezing-point depression constant.
m is the molality.
To calculate a solution's molality, divide the number of moles of solute by the mass of solvent (in kg).
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