Lithium forms compounds which are used in dry cells, storage batteries, and in high-temperature lubricants. It has two naturally occurring isotopes, 6Li (isotopic mass = 6.015123 amu) and 7Li (isotopic mass = 7.016005 amu). Lithium has an atomic mass of 6.9412 amu. What is the percent abundance of lithium-6? (Show work on your sheet).

To find the percent abundance of lithium-6, we will use the formula for the average atomic mass:

\[
\text{Atomic Mass} = (f_{\text{Li-6}} \times \text{mass of Li-6}) + (f_{\text{Li-7}} \times \text{mass of Li-7})
\]

Where:
- \( f_{\text{Li-6}} \) = fraction of lithium-6 isotope
- \( f_{\text{Li-7}} = 1 - f_{\text{Li-6}} \) (since the total abundance must equal 100%)
- Atomic mass of lithium = 6.9412 amu
- Mass of lithium-6 (\text{Li-6}) = 6.015123 amu
- Mass of lithium-7 (\text{Li-7}) = 7.016005 amu

### Step 1: Set up the equation

\[
6.9412 = (f_{\text{Li-6}} \times 6.015123) + [(1 - f_{\text{Li-6}}) \times 7.016005]
\]

### Step 2: Expand the equation

\[
6.9412 = f_{\text{Li-6}} \times 6.015123 + (1 - f_{\text{Li-6}}) \times 7.016005
\]

\[
6.9412 = f_{\text{Li-6}} \times 6.015123 + 7.016005 - f_{\text{Li-6}} \times 7.016005
\]

### Step 3: Combine like terms

\[
6.9412 = f_{\text{Li-6}} \times (6.015123 - 7.016005) + 7.016005
\]

\[
6.9412 = f_{\text{Li-6}} \times (-1.000882) + 7.016005
\]

### Step 4: Subtract 7.016005 from both sides

\[
6.9412 - 7.016005 = f_{\text{Li-6}} \times (-1.000882)
\]

\[
-0.074805 = f_{\text{Li-6}} \times (-1.000882)
\]

### Step 5: Solve for \( f_{\text{Li-6}} \)

\[
f_{\text{Li-6}} = \frac{-0.074805}{-1.000882}
\]

\[
f_{\text{Li-6}} = 0.074772
\]

So, the fraction of lithium-6 is approximately 0.074772.

### Step 6: Convert to percentage

\[
\text{Percent abundance of Li-6} = 0.074772 \times 100 = 7.48\%
\]

Thus, the percent abundance of lithium-6 is **7.48%**.

Would you like a further breakdown of any steps?

### Related Questions:
1. What is the percent abundance of lithium-7?
2. How does atomic mass affect the properties of elements?
3. Why is lithium used in high-temperature lubricants?
4. What is the difference between atomic mass and mass number?
5. How do isotopes influence the average atomic mass of an element?

### Tip: 
When solving problems with multiple isotopes, always remember the total abundance sums to 100%, and isolate variables step-by-step for clarity.

Solve a problem involving the calculation of the percent abundance of lithium-6 using isotopic masses and atomic mass. This solution involves isotopic abundance, weighted averages, and algebraic manipulation. Suitable for high school students in 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