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$\mathrm{\%}$ 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

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)

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: $$\frac{58.93}{M}=\frac{4.34}{100}$$

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: $$M=\frac{58.93\times 100}{4.34}$$

Calculate the Molar Mass

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

Key concepts

Vitamin B12

Vitamin B12, also known as cyanocobalamin, is a vital nutrient necessary for some of our bodily functions. Although found abundantly in animal tissues, it's pretty rare in higher plants. This vitamin plays a crucial role in the formation of red blood cells, DNA synthesis, and the normal functioning of our nervous system.
• It is essential for people who consume an entirely plant-based diet to monitor their Vitamin B12 levels, as they might not obtain enough of it from their food sources.
• Supplements or fortified foods are often advisable for them to prevent deficiency.
Vitamin B12 is needed in very small amounts, but even a slight deficiency can lead to serious health issues, such as anemia.

Cobalt Percentage

Cobalt is a significant microelement found in vitamin B12 and is crucial for its function in our body. In the form of cyanocobalamin used for Vitamin B12 supplements, cobalt makes up 4.34% of its molar mass.
• This percentage signifies that in every molecule of cyanocobalamin, one part is cobalt.
• The presence of cobalt is what allows cyanocobalamin to perform its role in creating new red blood cells and maintaining healthy nerve cells.
Understanding the cobalt percentage is important for calculating the total molar mass of cyanocobalamin, as it helps scientists and nutritionists ensure the proper dosage in supplements.

Deficiency Anemia

Deficiency anemia, specifically megaloblastic anemia, occurs when there are insufficient red blood cells or when they don't function properly due to a shortage of Vitamin B12. This type of anemia happens because the vitamin plays a major role in the production of these cells and DNA.
• Symptoms can include fatigue, headache, and weakness, often signaling the need for a closer look at nutritional intake.
• Long-term deficiency can lead to severe neurological issues and should be addressed promptly with dietary interventions or supplements.
For individuals avoiding animal products, such a deficiency can happen if alternative sources of Vitamin B12 are not consumed, making awareness and monitoring important.

Atomic Mass of Cobalt

The atomic mass of cobalt is an important factor when calculating the molar mass of any compound containing cobalt, such as cyanocobalamin. The atomic mass of cobalt is approximately 58.93 g/mol, which is found on the periodic table.
• This value helps us determine the contribution of cobalt to the overall molar mass of cyanocobalamin.
• Knowing the exact atomic mass is crucial for creating accurate nutritional supplements, ensuring people receive the correct amount of Vitamin B12.
In biochemistry, precise measurements are vital, and using cobalt's atomic mass correctly ensures that vitamin formulations lead to supplements that maintain proper health standards.