Question

Iodized salt contains a trace amount of calcium iodate, \(\mathrm{Ca}\left(\mathrm{IO}_{3}\right)_{2},\) to help prevent a thyroid condition called goiter. How many moles of iodine atoms are in \(0.500 \mathrm{~mol}\) of \(\mathrm{Ca}\left(\mathrm{IO}_{3}\right)_{2}\) ? How many grams of calcium iodate are needed to supply this much iodine?

Short answer

There are 1.00 mol of iodine atoms in 0.500 mol of calcium iodate. The mass of calcium iodate needed is approximately 389.94 grams.

Step-by-step solution

Determine the Moles of Iodine Atoms

To find the number of moles of iodine atoms, we need to know the mole ratio of iodine atoms to calcium iodate molecules. In the formula for calcium iodate, \(\mathrm{Ca}(\mathrm{IO}_{3})_{2}\), there are 2 iodine atoms for every molecule of calcium iodate. Therefore, the number of iodine atom moles is twice the number of calcium iodate moles. Multiply 0.500 moles of calcium iodate by 2 to find the moles of iodine atoms.

Calculate the Mass of Calcium Iodate

To find the mass of calcium iodate needed to supply 0.500 moles, first determine the molar mass of \(\mathrm{Ca}(\mathrm{IO}_{3})_{2}\). The molar mass of calcium iodate is the sum of the atomic masses of 1 calcium atom, 2 iodine atoms, and 6 oxygen atoms. Use the periodic table to find the atomic masses: Calcium=40.08 g/mol, Iodine=126.90 g/mol, Oxygen=16.00 g/mol. Calculate the molar mass: \(1 \times 40.08) + (2 \times 126.90) + (6 \times 16.00)\). Then, multiply the molar mass by the number of moles to find the grams of calcium iodate.

Key concepts

Mole Ratio

Understanding the mole ratio is crucial when dealing with chemical reactions and formulas. It indicates the proportion of reactants that react to form products. In our case, we are examining the substance calcium iodate calcium iodate (calcium iodate,. Each molecule of this compound contains two iodine atoms.

To find the number of moles of iodine atoms in a given number of moles of calcium iodate, we apply the mole ratio. For each mole of , there are essentially two moles of iodine atoms. This is represented as a 1:2 ratio. Therefore, if we have 0.500 moles of we will have 0.500 0.500. Therefore, if we have 0.500 moles of calcium iodate, we will have 0.500. Therefore, if we have 0.500 moles of calcium iodate (0.5000.500. Therefore, if we have 0.500 moles of calcium iodate, we will have 1.00 moles of iodine atoms (mol. This ratio is pivotal in stoichiometry, ensuring that the calculations for the amounts of reactants and products are accurate.

Molar Mass Calculation

Molar mass calculation is essential for converting between moles and grams, which is a common task in chemistry. The molar mass is the weight of one mole of a substance, measured in grams per mole (g/mol). To calculate the molar mass of calcium iodate, we sum the atomic masses of each element in the compound, each multiplied by the number of times that element appears in the chemical formula.

For calcium iodate (calcium iodate (calcium iodate (. For calcium iodate (calcium iodate (.\[\text{Molar mass of } \mathrm{Ca(IO_3)_2} = 1 \times 40.08 \, \text{g/mol} + 2 \times 126.90 \, \text{g/mol} + 6 \times 16.00 \, \text{g/mol}\]

Performing this calculation provides the molar mass of calcium iodate, which is essential for further calculations, such as determining how many grams are needed for a certain number of moles of the compound.

Stoichiometry

Stoichiometry is essentially the mathematics behind chemistry. It allows chemists to predict the amounts of substances consumed and produced in a given chemical reaction. Stoichiometric calculations are based on the balanced chemical equation and the concepts of the mole and molar mass.

Using stoichiometry, we can solve for quantities of reactants or products, as in our exercise, where the task is to calculate the grams of calcium iodate required to supply a certain amount of iodine atoms. This requires using the mole ratio to determine the number of moles of iodine atoms in relation to calcium iodate and then using the molar mass of calcium iodate to convert from moles to grams.

Stoichiometry hinges on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. This enables the precise calculation of reactant and product quantities through a balanced equation.

Chemical Formula

A chemical formula provides significant information about a compound, including the types and numbers of atoms present. For instance, the formula for calcium iodate is \( \mathrm{Ca(IO_3)_2} \), indicating that each unit of the compound contains one calcium atom, two iodine atoms, and six oxygen atoms.

These numbers are not arbitrary; they represent the fixed ratio in which elements combine to form the compound, reflecting the compound's stoichiometry. In a chemical formula, the subscript after an element symbol tells us how many atoms of that element are present in one molecule of the compound. No subscript implies the presence of only one atom of that element. Understanding the chemical formula is crucial for stoichiometric calculations, as it is the starting point for determining mole ratios and molar masses, which in turn are key for translating chemical reactions into quantifiable results.