Question

A salt is known to be an alkali metal fluoride. A quick approximate determination of the freezing point indicates that 4 g of the salt dissolved in 100 g of water produces a solution that freezes at about −1.4 °C. What is the formula of the salt? Show your calculations.

Short answer

The alkali metal fluoride with the nearest molecular mass is RbF having a molar mass of 105 g/mole.

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Step-by-step solution

Formula Mass

A molecular formula may be defined as the formula which gives information about the constituents present in the compound. The formula mass may be defined as the mass which depends upon the formula present. The original weight of a molecule may or may not be different.

Calculation of molar mass

\(\begin{aligned}{*{20}{l}}{{\rm{\Delta }}{{\rm{T}}_{\rm{f}}}{\rm{ = i \times }}{{\rm{K}}_{\rm{f}}}{\rm{ \times m}}}\\{{\rm{m = }}\frac{{{\rm{\Delta }}{{\rm{T}}_{\rm{f}}}}}{{{{\rm{K}}_{{\rm{f\;}}}}{\rm{ \times 2}}}}{\rm{\; }}}\\{{\rm{m = }}\frac{{{\rm{1}}{\rm{.}}{{\rm{4}}^{\rm{o}}}{\rm{C}}}}{{{\rm{2 \times 1}}{\rm{.8}}{{\rm{6}}^{\rm{o}}}{\rm{C}}{{\rm{m}}^{{\rm{ - 1}}}}}}{\rm{ }}}\\{{\rm{m = 0}}{\rm{.38m}}}\end{aligned}\)

\(Number{\rm{ }}of{\rm{ }}Moles{\rm{ }} = {\rm{ }}\frac{{Mass}}{{Molar{\rm{ }}Mass}}{\rm{ }}\)

\(\begin{aligned}{l}{\rm{Moles of fluoride = 0}}{\rm{.100 kg \times 0}}{\rm{.38 m = 0}}{\rm{.038 mol}}\\{\rm{Molar Mass = }}\frac{{{\rm{4g}}}}{{{\rm{0}}{\rm{.038mole}}}}{\rm{ = 105 gmol}}{{\rm{e}}^{{\rm{ - 1}}}}\end{aligned}\)

The alkali metal fluoride with the nearest molecular mass is RbF having molar mass = 105 g/mole.