Question

Vitamin B₁₂, cyanocobalamin, is essential for human nutrition. It is concentrated in animal tissuebut not in higher plants. Although nutritional requirements for the vitamin are quite low, peoplewho abstain completely from animal products may develop a deficiency anemia.Cyanocobalamin is the form used in vitamin supplements. It contains 4.34% cobalt by mass.Calculate the molar mass of cyanocobalamin, assuming that there is one atom of cobalt in everymolecule of cyanocobalamin.

Short answer

The molar mass of cyanocobalamin is 1359 g/mol.

Step-by-step solution

Given Information

Thecobalt’s mass percent is 4.34 %. This means that 4.34 g which is present in 100 g in cyanocobalamin. The atom number of Co present in 1 mol. The cyanocobalamin moles is 4.36 g Co. The cyanocobalamin moles are,

$4.34\mathrm{g}\mathrm{Co}\times \frac{1\mathrm{mol}\mathrm{Co}}{58.93\mathrm{g}\mathrm{Co}}\times \frac{1\mathrm{mol}\mathrm{Cyanocobala}\min }{1\mathrm{mol}\mathrm{Co}}=7.36\times {10}^{-2}\mathrm{mol}$

Calculating molar mass of cyanocobalamin

The molar mass of cyanocobalamin can be get by dividing its mass to moles.

$\begin{array}{rcl}\mathrm{Molar}\mathrm{mass}& =& \frac{100\mathrm{g}}{7.36\times {10}^{-2}\mathrm{mol}}\\ & =& 1359\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.\end{array}$

$\begin{array}{rcl}\mathrm{Molar}\mathrm{mass}& =& \frac{100\mathrm{g}}{7.36\times {10}^{-2}\mathrm{mol}}\\ & =& 1359\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.\end{array}$