https://file.aiquickdraw.com/mathbot/file/1728887598867os3vhcqn.jpg

Let's walk through the solution based on the given information.

### **Step 1: Find the mass of 1 mole of aluminum atoms (in grams).**

- **Mass of one aluminum atom**: \( 4.48 \times 10^{-23} \, \text{g} \)
- **Avogadro's number**: \( 6.022 \times 10^{23} \, \text{atoms/mol} \)

To get the mass of **1 mole** of aluminum atoms, multiply the mass of one atom by Avogadro's number:

\[
\text{Mass of 1 mole} = \left( 4.48 \times 10^{-23} \, \text{g} \right) \times \left( 6.022 \times 10^{23} \, \text{atoms/mol} \right)
\]

\[
\text{Mass of 1 mole} = 26.97 \, \text{g/mol}
\]

---

### **Step 2: Find how many moles of aluminum atoms equal the mass of the airplane.**

- **Mass of airplane**: \( 5000 \, \text{kg} \)
- **Convert to grams**: \( 5000 \, \text{kg} = 5.0 \times 10^6 \, \text{g} \)
- **Mass of 1 mole of aluminum**: \( 26.97 \, \text{g/mol} \)

Now, divide the total mass of the airplane by the mass of 1 mole of aluminum to get the number of moles:

\[
\text{Moles} = \frac{5.0 \times 10^6 \, \text{g}}{26.97 \, \text{g/mol}}
\]

\[
\text{Moles} \approx 1.85 \times 10^5 \, \text{mol}
\]

---

### **Answers:**

1. **Mass of 1 mole of aluminum atoms**: \( 26.97 \, \text{g} \)  
2. **Number of moles to equal airplane's mass**: \( 1.85 \times 10^5 \, \text{mol} \)

Would you like further details or have questions about any of these steps?

---

### **Related Questions:**

1. How is Avogadro’s number used in other chemical calculations?
2. What would the mass of 0.5 moles of aluminum be?
3. How do you convert between moles and grams for different elements?
4. Why is it important to use significant figures in chemistry?
5. How would the calculations change if the airplane weighed 2,500 kg?

---

**Tip:** Always make sure your units are consistent (e.g., converting kilograms to grams) to avoid calculation errors!

An aluminum atom has a mass of 4.48 × 10^−23 g, and a small airplane has a mass of 5000 kg. What is the mass of 1 mole of aluminum atoms? How many moles of aluminum atoms have a mass equal to the mass of a small airplane?

Learn how to calculate the mass of 1 mole of aluminum atoms using Avogadro's number and how to determine the number of moles equivalent to the mass of a small airplane. This step-by-step solution covers key concepts in chemistry, such as moles, unit conversion, and Avogadro's theorem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation