Problem 67 - Chemistry and Chemical Reactivity

Question

Analysis of a 10.0 -g sample of apatite (a major component of tooth enamel) showed that it was made up of \(3.99 \mathrm{g} \mathrm{Ca}, 1.85 \mathrm{g} \mathrm{P}, 4.14 \mathrm{g} \mathrm{O},\) and \(0.020 \mathrm{g} \mathrm{H} .\) I ist these elements based on relative amounts (moles), from smallest to largest.

Step-by-Step Solution

Answer

Elements in order: H, P, Ca, O.

Step 1: Determine Molar Masses of Elements

First, we need to know the molar mass (atomic weight) of each element present in the compound. The molar masses are approximately: - Calcium (Ca): 40.08 g/mol - Phosphorus (P): 30.97 g/mol - Oxygen (O): 16.00 g/mol - Hydrogen (H): 1.008 g/mol.

Step 2: Calculate Moles of Each Element

Now, we calculate the moles of each element using the formula: \[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]- Moles of Ca: \( \frac{3.99}{40.08} \approx 0.0997 \text{ moles} \)- Moles of P: \( \frac{1.85}{30.97} \approx 0.0597 \text{ moles} \)- Moles of O: \( \frac{4.14}{16.00} \approx 0.25875 \text{ moles} \)- Moles of H: \( \frac{0.020}{1.008} \approx 0.0198 \text{ moles} \).

Step 3: Compare Moles to Determine Order

With the moles calculated, arrange the elements based on quantity in ascending order: 1. Hydrogen (H): 0.0198 moles 2. Phosphorus (P): 0.0597 moles 3. Calcium (Ca): 0.0997 moles 4. Oxygen (O): 0.25875 moles.

Key Concepts

Molar Mass Calculation

When you're trying to unravel the composition of a compound, you'll first need to determine the molar mass of each element present. The molar mass is simply the mass of one mole of a given substance and is typically expressed in grams per mole (g/mol).

You can find these values on the periodic table and they reflect the average mass of the atoms in naturally occurring samples. Here's a look at the molar masses for the elements in apatite, which were used in this exercise:

• Calcium (Ca): 40.08 g/mol
• Phosphorus (P): 30.97 g/mol
• Oxygen (O): 16.00 g/mol
• Hydrogen (H): 1.008 g/mol

These molar masses allow us to translate a sample's mass into moles, helping us understand how much of each element is present in our compound.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with relationships between the quantities of reactants and products in a chemical reaction. In this context, stoichiometry helps in determining the relative quantities of elements in a compound.

By using stoichiometry, chemically equivalent quantities can be compared. For example, in this exercise, by knowing the mass of each element in the apatite sample and their molar masses, we performed stoichiometric calculations to convert grams into moles. This approach allows students to better understand the quantitative relationships in a sample.

Moles of Elements

The concept of "moles" is integral to chemistry, providing a bridge between the atomic and macroscopic worlds. The mole allows chemists to count particles by weighing them. To calculate the number of moles, the formula is:

• \[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]

In our exercise, we applied this formula to convert the given mass of each element into moles:

• For Calcium (Ca): \( \frac{3.99}{40.08} = 0.0997 \text{ moles} \)
• For Phosphorus (P): \( \frac{1.85}{30.97} = 0.0597 \text{ moles} \)
• For Oxygen (O): \( \frac{4.14}{16.00} = 0.25875 \text{ moles} \)
• For Hydrogen (H): \( \frac{0.020}{1.008} = 0.0198 \text{ moles} \)

Calculating moles is an essential step in analyzing the composition of compounds, determining the proportion of each element within the compound.

Compound Composition Analysis

Compound composition analysis allows chemists to understand what is within a sample and in what quantities. This analysis often involves breaking down the compound into its constituent elements and comparing their relative amounts.

In the case of apatite, after determining the moles of each element, we arranged them in ascending order based on their mole quantities:

• Hydrogen (H) was the smallest with 0.0198 moles.
• Phosphorus (P) came next with 0.0597 moles.
• Calcium (Ca) was larger with 0.0997 moles.
• Oxygen (O) had the most at 0.25875 moles.

Analyzing the composition of a compound in such a manner provides a detailed picture of its makeup, crucial for various applications, including chemical synthesis and material sciences.