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Chapter 3: Problem 121

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

Write down the given information

- Percentage by mass of cobalt: 4.34% - Molar mass of cobalt (Co): 58.93 g/mol
02

Write down the formula

Mass percentage of cobalt = \( \frac{\text{Molar mass of cobalt in cyanocobalamin}}{\text{Molar mass of cyanocobalamin}} \) * 100
03

Substitute the known values in the formula

4.34 = \( \frac{58.93}{\text{Molar mass of cyanocobalamin}} \) * 100
04

Solve for the molar mass of cyanocobalamin

First, divide both sides by 100: 0.0434 = \( \frac{58.93}{\text{Molar mass of cyanocobalamin}} \) Now, multiply both sides by the molar mass of cyanocobalamin. This will give us: 0.0434 * (Molar mass of cyanocobalamin) = 58.93 Finally, divide both sides by 0.0434 to find the molar mass of cyanocobalamin: Molar mass of cyanocobalamin = \( \frac{58.93}{0.0434} \) Molar mass of cyanocobalamin = 1357.603 g/mol Since molar mass should generally be represented with one decimal place, we can round the molar mass to 1357.6 g/mol. This is the molar mass of cyanocobalamin, Vitamin B12.

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