Question

Vitamin \(\mathrm{B}_{12}\) is a coordination compound with cobalt as its central atom. It contains \(4.4 \%\) cobalt by mass and has a molar mass of \(1.3 \times\) \(10^{3} \mathrm{~g} / \mathrm{mol}\). How many cobalt atoms are in a molecule of vitamin \(\mathrm{B}_{12} ?\)

Short answer

Answer: 1 cobalt atom is present in one molecule of vitamin B12.

Step-by-step solution

Calculate the mass of cobalt in one mole of vitamin B12

Given that vitamin B12 contains 4.4% cobalt by mass, we can find the mass of cobalt present in one mole of vitamin B12. To do this, we'll multiply the molar mass of vitamin B12 by the percentage of cobalt. Mass of cobalt in one mole of vitamin B12 = (Molar mass of vitamin B12) x (percentage of cobalt) = \(1.3 \times 10^{3} \mathrm{~g/mol} \times 0.044\) = \(57.2 \mathrm{~g}\)

Calculate the moles of cobalt in one mole of vitamin B12

Now that we have the mass of cobalt in one mole of vitamin B12, we can use the molar mass of cobalt to find the number of moles of cobalt present. The molar mass of cobalt is approximately 58.93 g/mol. Moles of cobalt in one mole of vitamin B12 = \(\frac{\text{mass of cobalt}}{\text{molar mass of cobalt}}\) = \(\frac{57.2 \mathrm{~g}}{58.93 \mathrm{~g/mol}}\) = \(0.970 \mathrm{~mol}\)

Calculate the number of cobalt atoms in one molecule of vitamin B12

Finally, to find out the number of cobalt atoms in one molecule of vitamin B12, we'll multiply the number of moles of cobalt by Avogadro's number (approximately \(6.022 \times 10^{23}\) atoms/mol). Number of cobalt atoms in one molecule of vitamin B12 = (moles of cobalt) x (Avogadro's number) = \(0.970 \mathrm{~mol} \times 6.022 \times 10^{23} \mathrm{~atoms/mol}\) = \(5.84 \times 10^{23} \mathrm{~atoms}\) However, it's important to remember that the number of atoms must be a whole number, so we need to round this result to the nearest whole number: Number of cobalt atoms in one molecule of vitamin B12 = 1 atom. Thus, there is 1 cobalt atom in a molecule of vitamin B12.

Key concepts

Coordination Compound

Vitamin B12 is a fascinating example of a coordination compound. These compounds can be thought of as a central atom or ion, surrounded by molecules or ions that are bonded to it in a specific geometric pattern. In the case of vitamin B12, the central atom is cobalt.
Coordination compounds are vital in many biological processes, and vitamin B12 plays a crucial role in human health, notably in the production of red blood cells and the maintenance of the nervous system. The cobalt in vitamin B12 is coordinated with various atoms and groups, giving the compound its unique properties and functionality.

Molar Mass Calculation

Calculating the molar mass of a compound involves determining the sum of the molar masses of all the elements in one mole of the compound. In the case of vitamin B12, the molar mass is given as 1300 g/mol. This means that if you have one mole of vitamin B12, it will weigh 1300 grams.
To find out how many grams of cobalt are present in vitamin B12, we use the percentage of cobalt by mass. By multiplying 1300 g/mol by 4.4%, we find that there are 57.2 grams of cobalt in one mole of vitamin B12. This process helps in converting between moles and grams, a common requirement in chemistry.

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry and is approximately equal to \(6.022 \times 10^{23}\) particles/mol. This number allows chemists to convert between the number of atoms, molecules, or ions and the amount of substance in moles.
For vitamin B12, using Avogadro's number helps us determine how many cobalt atoms are present in a given mole of the substance. By calculating the moles of cobalt and multiplying by Avogadro's number, we find out that there exists approximately one cobalt atom per molecule of vitamin B12, demonstrating the power of this constant in bridging the microscopic and macroscopic worlds of chemistry.

Cobalt in Vitamin B12

Cobalt is the central metal atom in vitamin B12, making it a key player in this molecule's structure and function. This metal ion is essential not only in sustaining the geometry needed for the vitamin's biological activity but also for the chemistry that occurs in the body.
While cobalt itself is a transition metal, the way it is integrated into vitamin B12 allows it to participate in various biochemical processes, such as acting as a catalyst in enzyme reactions. Moreover, the presence of cobalt gives vitamin B12 its distinctive red color, an indicator of its coordination chemistry. Understanding the role of cobalt is vital in appreciating the intricate nature of vitamin B12 and its significant contributions to health.