Question

How many grams of calcium must be combined with \(1 \mathrm{~g}\) phosphorus to form the compound \(\mathrm{Ca}_{3} \mathrm{P}_{2}\) ?

Short answer

1.938 grams of calcium

Step-by-step solution

Identify the molecular compound

The compound formed is \(\text{Ca}_{3}\text{P}_{2}\).

Find the molar mass of the compound

Calculate the molar masses: Calcium (Ca) has a molar mass of 40 g/mol and Phosphorus (P) has a molar mass of 31 g/mol. The molar mass of \(\text{Ca}_{3}\text{P}_{2}\) is: \[ 3 \times 40 \text{ g/mol} + 2 \times 31 \text{ g/mol} = 120 \text{ g/mol of Ca} + 62 \text{ g/mol of P} = 182 \text{ g/mol} \]

Calculate the moles of phosphorus

Using the mass given, calculate moles of phosphorus: \[ \text{Moles of P} = \frac{1 \text{ g}}{31 \text{ g/mol}} = 0.0323 \text{ moles} \]

Determine the moles of calcium required

From the chemical formula \(\text{Ca}_{3}\text{P}_{2}\), 2 moles of phosphorus require 3 moles of calcium. Hence, \[ \text{Moles of Ca} = 0.0323 \text{ moles P} \times \frac{3 \text{ moles Ca}}{2 \text{ moles P}} = 0.04845 \text{ moles} \]

Calculate the mass of calcium required

Finally, convert the moles of calcium to mass: \[ \text{Mass of Ca} = 0.04845 \text{ moles} \times 40 \text{ g/mol} = 1.938 \text{ g} \]

Key concepts

molar mass calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate it, you need to add up the atomic masses of all the atoms in a molecule. This is crucial for stoichiometry, as it allows you to convert between grams and moles.
For example, in the compound \(\text{Ca}_{3}\text{P}_{2}\), you calculate the molar mass by adding the masses of 3 calcium atoms and 2 phosphorus atoms.
The steps to calculate the molar mass of \(\text{Ca}_{3}\text{P}_{2}\) are:

• Calcium (Ca): 40 g/mol
• Phosphorus (P): 31 g/mol

So, the total molar mass is:
\[ 3 \times 40 \text{ g/mol} + 2 \times 31 \text{ g/mol} = 182 \text{ g/mol} \] This tells you that one mole of \(\text{Ca}_{3}\text{P}_{2} \) weighs 182 grams.

moles conversion

Conversion between moles and grams is a common task in chemistry. This requires using the molar mass of a substance. Here's how you can convert between these units:
Suppose you have 1 gram of phosphorus (P). To find out how many moles this represents, you use the molar mass of phosphorus:

• Molar mass of P: 31 g/mol

Using the formula:
\[\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}\]
we get:
\[ \frac{1 \text{ g}}{31 \text{ g/mol}} = 0.0323 \text{ moles} \]
So, 1 gram of phosphorus equals 0.0323 moles.
This is useful for determining how much of another element is needed to react with these moles. For example, in \(\text{Ca}_{3}\text{P}_{2}\), 2 moles of phosphorus react with 3 moles of calcium. This ratio helps convert the moles of phosphorus into moles of calcium needed.

chemical compounds

Chemical compounds are substances composed of two or more different elements, chemically bonded together. The compound we are interested in is \(\text{Ca}_{3}\text{P}_{2}\). Here's what you should know:
\(\text{Ca}_{3}\text{P}_{2}\) stands for calcium phosphide.
Each molecule contains 3 calcium (Ca) atoms and 2 phosphorus (P) atoms.

• This tells us the stoichiometric ratio: 3 moles of Ca are needed for 2 moles of P.
• Knowing this ratio is crucial for calculating how much of each element you need to form the compound.

In our example, to find out how much calcium you need to react with 1 gram of phosphorus, follow these steps:

• Calculate the moles of phosphorus: 0.0323 moles
• Use the stoichiometric ratio to find moles of calcium: 0.0323 mol P \(\times \frac{3 \text{ moles Ca}}{2 \text{ moles P}} \) = 0.04845 mol Ca
• Convert moles of calcium to grams using its molar mass: 0.04845 mol \(\times 40 \text{ g/mol} \)= 1.938 g

This means you need 1.938 grams of calcium to fully react with 1 gram of phosphorus to form \(\text{Ca}_{3}\text{P}_{2}\).