Determining the Number of Moles of Calcium Carbonate and Barium Carbonate Containing Specific Moles of Oxygen

Understanding the relationship between the number of moles of a compound and the corresponding moles of its constituent atoms is crucial in chemistry. This principle is particularly useful in solving stoichiometric problems, such as determining the amount of a compound needed to achieve a specific number of moles of one of its constituent atoms. In this article, we will explore the calculations required to determine the number of moles of calcium carbonate (CaCO?) and barium carbonate (BaCO?) that contain a specific number of moles of oxygen atoms.

Calculation for Calcium Carbonate (CaCO?)

Let's begin with the compound calcium carbonate (CaCO?). Every molecule of CaCO? contains 3 oxygen atoms. Therefore, if we want to find the number of moles of CaCO? that contain 1.5 moles of oxygen atoms, we can follow these steps:

Identify the number of oxygen atoms in each molecule of CaCO?: 3 oxygen atoms per molecule. Let n represent the number of moles of CaCO?. The total number of moles of oxygen in n moles of CaCO? can be calculated using the formula:

Moles of O 3n

Set this equal to the given number of moles of oxygen (1.5 moles):

3n 1.5

Solve for n by dividing both sides by 3:

n 1.5 / 3 0.5

Therefore, 0.5 moles of CaCO? will contain 1.5 moles of oxygen atoms.

Calculation for Barium Carbonate (BaCO?)

Now, let's consider barium carbonate (BaCO?). Similarly, every molecule of BaCO? contains 3 oxygen atoms. To find the number of moles of BaCO? that contain 1.5 moles of oxygen atoms, we can use a similar approach:

Identify the number of oxygen atoms in each molecule of BaCO?: 3 oxygen atoms per molecule. Let x represent the number of moles of BaCO?. The total number of moles of oxygen in x moles of BaCO? can be calculated using the formula:

Moles of O 3x

Set this equal to the given number of moles of oxygen (1.5 moles):

3x 1.5

Solve for x by dividing both sides by 3:

x 1.5 / 3 0.5

Therefore, 0.5 moles of BaCO? will contain 1.5 moles of oxygen atoms.

Generalizing the Relationship

From the above calculations, we can derive a general rule. If 1 mole of a compound contains a certain number of moles of oxygen atoms, then to find the number of moles of the compound that contain a specific number of moles of oxygen atoms, we can use the following formula:

Moles of compound Moles of oxygen / Moles of oxygen per mole of compound

Additional Insights

It is also important to note that the process of determining the number of moles of a compound based on the number of moles of one of its constituent atoms can be used to solve a variety of stoichiometric problems. For instance, if we consider another compound like BaCO?, we can use the same approach to determine the number of moles of any other element in the compound, such as barium (Ba) or carbon (C), if given the number of moles of oxygen atoms. This can be particularly useful in real-world applications where precise chemical calculations are necessary.

Conclusion

In summary, understanding the relationship between the number of moles of a compound and the corresponding moles of its constituent atoms is key to solving stoichiometric problems. The calculations presented here for calcium carbonate (CaCO?) and barium carbonate (BaCO?) demonstrate a straightforward method to determine the number of moles of a compound that contains a specific number of moles of oxygen atoms. These principles can be applied to a wide range of chemical compounds and contribute to a deeper understanding of chemical stoichiometry.