Vitamin \(\mathrm{B}_{12},\) cyanocobalamin, is essential for human nutrition. It is concentrated in animal tissue but not in higher plants. Although nutritional requirements for the vitamin are quite low, people who 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 every molecule of cyanocobalamin.

Short Answer

Expert verified
The molar mass of cyanocobalamin (Vitamin B12) is approximately 1357.6 g/mol.

Step by step solution

01

Collect Information Given

We have the following information: - Cobalt Percentage in cyanocobalamin: 4.34% - Atomic mass of cobalt: 58.93 g/mol (found on the periodic table)
02

Set up an Equation to Calculate the Molar Mass of Cyanocobalamin

Let M be the molar mass of cyanocobalamin. We are given that the mass of cobalt in cyanocobalamin is 4.34% of the total molar mass. So, we can set up the equation: \[ \frac{58.93}{M} = \frac{4.34}{100} \]
03

Solve the Equation for the Molar Mass

To isolate M, we can cross-multiply: \[ 58.93 \times 100 = 4.34 \times M \] Now, divide both sides by 4.34 to find the molar mass of cyanocobalamin: \[ M = \frac{58.93 \times 100}{4.34} \]
04

Calculate the Molar Mass

Plugging the given values into the equation, we can find the molar mass of cyanocobalamin: \[ M = \frac{58.93 \times 100}{4.34} = 1357.6\, g/mol \] The molar mass of cyanocobalamin (Vitamin B12) is approximately 1357.6 g/mol.

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