Question

Calcium carbonate is the active ingredient in some antacids. It is also the compound in the mineral known as calcite. How many moles of calcium carbonate are present in a chewable table that contains \(750.0 \mathrm{mg} \mathrm{CaCO}_{3}\) ?

Short answer

The number of moles of calcium carbonate present in the tablet is \(0.00749\,mol\)

Step-by-step solution

Conversion of milligrams to grams

The mass of calcium carbonate is presented in milligrams. However, the molar mass is always given in grams per mole. Thus, first convert the mass of calcium carbonate from milligrams to grams. One gram is equal to 1000 milligrams, so we divide the initial mass by 1000: \(750.0\,mg = 750.0/1000\,g = 0.75\,g\)

Determination of molar mass

The molar mass is the mass of a given substance divided by the amount of substance. The amount is measured in moles. In order to find the molar mass of calcium carbonate, \(CaCO_3\), sum up the molar masses of each element found in the chemical formula, given that the molar mass of Ca, C and O are 40.08 g/mol, 12.01 g/mol and 16.00 g/mol respectively. So, the molar mass of calcium carbonate is \(40.08 + 12.01 + 3*(16.00) = 100.09\,g/mol\)

Calculation of number of moles

Knowing the mass of the substance and its molar mass, moles of the substance can be calculated using equation: number of moles = mass / molar mass. Therefore, for this case, number of moles of calcium carbonate = \(0.75\,g / 100.09\,g/mol = 0.00749\,mol\)

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that helps us understand the amount of a substance in terms of its number of moles. It tells us how much one mole of a substance weighs and is measured in grams per mole (g/mol). When calculating molar mass, we sum up the atomic masses of all the individual elements present in the chemical formula of a compound. For example, calcium carbonate (\(CaCO_3\)) is made up of calcium (Ca), carbon (C), and oxygen (O). The atomic masses are approximately:

• Calcium: 40.08 g/mol
• Carbon: 12.01 g/mol
• Oxygen: 16.00 g/mol

To find the molar mass of \(CaCO_3\), add up these values, making sure to account for all atoms:\[40.08\, \text{(Ca)} + 12.01\, \text{(C)} + 3\times16.00\, \text{(O)} = 100.09\, \text{g/mol}\]This total represents the molar mass of calcium carbonate, allowing us to connect its mass in grams to its quantity in moles.

Moles Calculation

Understanding how to calculate moles is essential for tasks ranging from stoichiometry problems to chemical reactions. It involves using the mass of a substance and its molar mass to find out how many moles you have. Here's the simple formula to remember:\[\text{Number of moles} = \frac{\text{Mass of substance (g)}}{\text{Molar mass (g/mol)}}\]Let's look at the example of calcium carbonate (\(CaCO_3\)) mentioned in the exercise. Suppose we're given 0.75 grams of \(CaCO_3\). Knowing its molar mass is 100.09 g/mol, we can find the number of moles in the tablet:\[0.75\, \text{g} \div 100.09\, \text{g/mol} = 0.00749\, \text{mol}\]This means there are 0.00749 moles of calcium carbonate in the tablet, which is crucial for calculating the compound's participatory element in reactions or formulations.

Chemical Formula

The chemical formula of a compound tells you the specific elements in the molecule and the ratio of these elements. It is like a recipe that guides you on what makes up a compound.When we say calcium carbonate is \(CaCO_3\), it indicates:

• 1 atom of calcium (Ca)
• 1 atom of carbon (C)
• 3 atoms of oxygen (O)

This formula helps in calculating molar mass by informing us how many atoms of each element are present, making it possible to sum their atomic masses correctly.Additionally, chemical formulas help us understand how compounds will react in chemical equations. For example, knowing the formula \(CaCO_3\) in a reaction allows prediction of products resulting from reactions like decomposition, where \(CaCO_3\) might become \(CaO\) and \(CO_2\) when heated. Understanding the chemical formula is fundamental for predicting behavior and interactions in chemistry.