Question

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

The molar mass of cyanocobalamin, Vitamin B12, is approximately 1357.6 g/mol.

Step-by-step solution

Write down the given information

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

Write down the formula

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

Substitute the known values in the formula

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

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.

Key concepts

Cyanocobalamin

Cyanocobalamin is a synthetic form of Vitamin B12, often used in dietary supplements and fortified foods. It plays an essential role in ensuring that the body functions properly. While the term may sound complex, it mainly serves as a source of Vitamin B12 for those who need it.
Cyanocobalamin is stabilized by the addition of cyanide, hence the prefix 'cyano'. This tiny amount of cyanide is harmless and allows the Vitamin B12 to be shelf-stable.
For individuals who do not consume meat or other animal products, cyanocobalamin can help fill the gap. It is safe and widely used in multivitamins and B12 supplements to prevent deficiencies.

Vitamin B12

Vitamin B12, scientifically known as cobalamin, is a crucial vitamin that helps in producing DNA and maintaining nerve health. It is uniquely found in animal products, which means people on vegetarian or vegan diets might struggle to get enough.
Pivotal roles of Vitamin B12 include:

• Red blood cell formation
• Neurological function
• DNA synthesis

Vitamin B12 is stored in the liver, and although the body requires small amounts, a deficiency can lead to significant health issues. This is why supplements and fortified foods containing cyanocobalamin are essential for some people.

Percentage Composition

Percentage composition refers to the percentage by mass of each element present in a compound. For cyanocobalamin, knowing the percentage composition is vital to determine its overall molar mass.
Let's break it down with cyanocobalamin's formula:

• The percentage of cobalt is given as 4.34%.
• By understanding this data, along with the known mass of cobalt, we can pinpoint the molar mass of the entire compound.

This calculation involves using the formula:
\[\text{Mass percentage of cobalt} = \frac{\text{Molar mass of cobalt in cyanocobalamin}}{\text{Molar mass of cyanocobalamin}} \times 100\]
By substituting the known values, we determined that the molar mass of cyanocobalamin is 1357.6 g/mol.

Deficiency Anemia

Deficiency anemia can occur when the body doesn't have enough Vitamin B12. This condition affects red blood cell production, leading to various health issues.
Without enough B12, red blood cells can't properly develop into full-sized, healthy cells, resulting in a reduced ability to carry oxygen. People may experience:

• Fatigue
• Weakness
• Nerve damage

Anyone completely abstaining from animal products is at higher risk for Vitamin B12 deficiency anemia.
Supplementation with cyanocobalamin is an effective prevention strategy, allowing individuals to maintain healthy blood cell production and neurological function.