Question

What mass of calcium (Ca, atomic mass \(=40.08 \mathrm{~g} / \mathrm{mole}\) ) must be combined with \(1.00 \mathrm{~g}\) of phosphorus \((\mathrm{P}\), atomic mass \(=30.97 \mathrm{~g} /\) mole \()\) to form the compound \(\mathrm{Ca}_{3} \mathrm{p}_{2} ?\)

Short answer

1.94 grams of calcium must be combined with 1.00 grams of phosphorus to form the compound Ca3P2.

Step-by-step solution

Convert mass of phosphorus to moles

To convert the mass of phosphorus (1.00 g) to moles, we will divide the mass by its atomic mass (30.97 g/mole), as follows: \[ \text{moles of phosphorus} = \frac{\text{mass of phosphorus}}{\text{atomic mass of phosphorus}} = \frac{1.00 \text{ g}}{30.97 \frac{\text{g}}{\text{mole}}} \]

Calculate the mole ratio between calcium and phosphorus

Now we need to find the mole ratio of calcium to phosphorus in the compound Ca3P2. To do this, we will look at the subscripts in the chemical formula: there are 3 moles of calcium for every 2 moles of phosphorus. Mole ratio of Ca : P = 3 : 2

Convert moles of phosphorus to moles of calcium

Next, we will use the mole ratio to convert the moles of phosphorus to moles of calcium. To do this, we will multiply the moles of phosphorus by the mole ratio, as follows: \[ \text{moles of calcium} = \text{moles of phosphorus} \times \frac{\text{moles of Ca}}{\text{moles of P}} \]

Convert moles of calcium to mass of calcium

Finally, we will convert the moles of calcium to mass of calcium. To do this, we will multiply the moles of calcium by the atomic mass of calcium (40.08 g/mole), as follows: \[ \text{mass of calcium} = \text{moles of calcium} \times \text{atomic mass of calcium} \] Now, let's put everything together: \[ \text{mass of calcium} = \left(\frac{1.00 \text{ g}}{30.97 \frac{\text{g}}{\text{mole}}} \right) \left(\frac{3 \text{ moles of Ca}}{2 \text{ moles of P}}\right) \left(40.08 \frac{\text{g}}{\text{mole}}\right) \] \[ \text{mass of calcium} = 1.94 \text{ g} \] Therefore, 1.94 grams of calcium must be combined with 1.00 grams of phosphorus to form the compound Ca3P2.

Key concepts

Mole Conversion

Mole conversion is like a translator for chemistry. It helps you convert between the mass of a substance and the number of moles, which is a unit that tells us how many atoms or molecules are in a sample. To do a mole conversion, you need to know the atomic or molar mass of the element from the periodic table.
For example, to convert grams of phosphorus to moles, you divide the mass of phosphorus by its atomic mass. The formula is:

• Moles of phosphorus = \( \frac{\text{mass of phosphorus}}{\text{atomic mass of phosphorus}} \)

This tells you how many moles are present in the 1 gram of phosphorus you started with. It’s an essential step before moving onto other calculations in stoichiometry.

Chemical Formulas

Chemical formulas are like recipes. They tell us how many atoms of each element are in a compound.
In the formula \( \text{Ca}_3\text{P}_2 \), it indicates that for every molecule of the compound, there are 3 calcium atoms and 2 phosphorus atoms.
These subscripts let you know in what ratio the elements are combined to form a stable compound. Understanding the chemical formula is pivotal because it helps you determine the mole ratios needed for calculating how much of each reactant is necessary to form a desired product.

Mole Ratio

A mole ratio comes from the coefficients of a balanced chemical equation or the subscripts in a chemical formula. It describes the proportions of reactants and products involved in a chemical reaction.
For \( \text{Ca}_3\text{P}_2 \), the mole ratio is 3:2, meaning for every 2 moles of phosphorus, 3 moles of calcium are needed.
Using mole ratios, you can convert moles of one substance to moles of another. For example, if you know moles of phosphorus, you use the mole ratio to find how many moles of calcium are needed. It acts as a map that guides you through chemical equations.

Atomic Mass

Atomic mass is the weight of a single atom of a chemical element and is typically listed on the periodic table. It’s measured in atomic mass units (u), but for practical calculations, it's expressed in grams per mole (g/mole).
This is important because it allows you to use a given mass and convert it to moles, which is essential for calculations you do in stoichiometry.
In our example, the atomic masses are given as 40.08 g/mole for calcium and 30.97 g/mole for phosphorus. By using these values, you can convert between mass and moles, determining how much of each reactant is needed and ensuring the chemistry works out just right!