Molar fraction and molality of a solution (8298)

, por F_y_Q

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A solution contains 36\ \% by mass of HCl:

a) Calculate the molar fraction of HCl.

b) Calculate the molality of HCl in the solution.

P.-S.

You can fix an amount of 100 g of solution to solve the problem because, in those 100 g of solution, there will be 36 g of HCl (which is what the percentage means) and 64 g of water. Convert both quantities to moles:

36\ \cancel{g}\ \ce{HCl}\cdot \frac{1\ mol}{36.5\ \cancel{g}}= \color[RGB]{0,112,192}{\textbf{0.986\ \ce{mol\ HCl}}}

64\ \cancel{g}\ \ce{H2O}\cdot \frac{1\ mol}{18\ \cancel{g}}= \color[RGB]{0,112,192}{\textbf{3.556\ \ce{mol\ H2O}}}

a) Calculate the molar fraction:

x_{\ce{HCl}}= \frac{n_{\ce{HCl}}}{n_{\ce{HCl}} + n_{\ce{H2O}}} = \frac{0.986\ \cancel{mol}}{(0.986 + 3.556)\ \cancel{mol}} = \fbox{\color[RGB]{192,0,0}{\bf 0.217}}


b) Calculate the molality. This is defined as the ratio between the moles of solute and the mass of solvent, expressed in kilograms:

m = \frac{n_{\ce{HCl}}}{m_{\ce{H2O}}\ (kg)} = \frac{0.986\ mol}{6.4\cdot 10^{-2}\ kg}= \fbox{\color[RGB]{192,0,0}{\bm{15.4\ \frac{mol}{kg}}}}