How many total moles of a) protons, b) neutrons and c) electrons are in 5.67x1026 atoms of Ca-48 in its most common
ionic form?

To solve this problem, we need to calculate the number of moles of protons, neutrons, and electrons in 5.67 × 10²⁶ atoms of the isotope Calcium-48 (Ca-48) in its most common ionic form. Here's the breakdown of the steps:

### Step 1: Understanding the isotope Ca-48

The atomic number of calcium (Ca) is 20. This means that:
- **Number of protons** = 20 for Ca.
- The isotope Ca-48 means that the mass number is 48. This mass number represents the sum of protons and neutrons. Therefore, the **number of neutrons** = 48 - 20 = 28.

Now, for a neutral atom of calcium:
- **Number of electrons** = 20 (equal to the number of protons).

However, the most common ionic form of calcium is **Ca²⁺**, which means it loses 2 electrons. So:
- **Number of electrons in Ca²⁺ ion** = 20 - 2 = 18.

### Step 2: Moles of atoms

We are given 5.67 × 10²⁶ atoms of Ca-48. To find the moles of atoms, we use Avogadro's number (\(6.022 \times 10^{23}\)):

\[
\text{moles of atoms} = \frac{5.67 \times 10^{26}}{6.022 \times 10^{23}} \approx 941.85 \text{ moles}
\]

### Step 3: Moles of protons, neutrons, and electrons

- **Protons**: Each Ca-48 atom has 20 protons. So the total moles of protons:
  \[
  \text{moles of protons} = 941.85 \text{ moles of atoms} \times 20 = 18,837 \text{ moles of protons}
  \]

- **Neutrons**: Each Ca-48 atom has 28 neutrons. So the total moles of neutrons:
  \[
  \text{moles of neutrons} = 941.85 \text{ moles of atoms} \times 28 = 26,372 \text{ moles of neutrons}
  \]

- **Electrons**: In the Ca²⁺ ion, there are 18 electrons per ion. So the total moles of electrons:
  \[
  \text{moles of electrons} = 941.85 \text{ moles of atoms} \times 18 = 16,953 \text{ moles of electrons}
  \]

### Final Answer:
- **a) Moles of protons** = 18,837 moles
- **b) Moles of neutrons** = 26,372 moles
- **c) Moles of electrons** = 16,953 moles

Would you like further clarification or more details on any of the steps?

### Relative questions:
1. How is Avogadro’s number used in converting atoms to moles?
2. Why does the most common ionic form of calcium have 18 electrons?
3. How would the moles of protons, neutrons, and electrons change if the isotope were Ca-40 instead of Ca-48?
4. How do you calculate the number of neutrons in an isotope?
5. Why does the number of protons define the element, and not the number of neutrons or electrons?

### Tip:
Always verify the most common ionic form of an element, as it can impact the number of electrons significantly in these types of calculations.

How many total moles of a) protons, b) neutrons and c) electrons are in 5.67x10²⁶ atoms of Ca-48 in its most common ionic form?

This detailed solution explains how to calculate the moles of protons, neutrons, and electrons in 5.67x10²⁶ atoms of the isotope Ca-48 in its Ca²⁺ ionic form. Using Avogadro's number and atomic structure, the problem involves key concepts in mole calculations and stoichiometry. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation