Average atomic mass of magnesium is 24.31 amu. This magnesium is composed of 79 mole ` %` of `.^(24)Mg` and remaining 21 mol `%` of `.^(25)Mg` and `.^(26)Mg`. Calculate mole `%` of `.^(26)Mg`.

Options

A. 10
B. 11
C. 15
D. 16

Answer

To solve the problem, we need to calculate the mole percentage of the isotope \(^ {26}Mg\) given the average atomic mass of magnesium and the mole percentages of the other isotopes. Here's a step-by-step solution:

### Step 1: Understand the given data
- Average atomic mass of magnesium = 24.31 amu
- Mole percentage of \(^ {24}Mg\) = 79%
- Remaining mole percentage (for \(^ {25}Mg\) and \(^ {26}Mg\)) = 21%

### Step 2: Define the variables
Let:
- The mole percentage of \(^ {25}Mg\) = \(x\)
- The mole percentage of \(^ {26}Mg\) = \(21 - x\)

### Step 3: Write the average atomic mass equation
The average atomic mass can be calculated using the formula:
\[ \text{Average atomic mass} = \left( \text{mass of } ^{24}Mg \times \text{mole \% of } ^{24}Mg \right) + \left( \text{mass of } ^{25}Mg \times \text{mole \% of } ^{25}Mg \right) + \left( \text{mass of } ^{26}Mg \times \text{mole \% of } ^{26}Mg \right) \]
Substituting the known values:
\[ 24.31 = \left( 24 \times 0.79 \right) + \left( 25 \times \frac{x}{100} \right) + \left( 26 \times \frac{21 - x}{100} \right) \]

### Step 4: Simplify the equation
Calculating the first term:
\[ 24 \times 0.79 = 18.96 \]
Now, substituting this into the equation:
\[ 24.31 = 18.96 + \frac{25x + 26(21 - x)}{100} \]
Expanding the equation:
\[ 24.31 = 18.96 + \frac{25x + 546 - 26x}{100} \]
Combining like terms:
\[ 24.31 = 18.96 + \frac{546 - x}{100} \]

### Step 5: Isolate \(x\)
Multiply through by 100 to eliminate the fraction:
\[ 2431 = 1896 + 546 - x \]
Rearranging gives:
\[ x = 1896 + 546 - 2431 \]
Calculating the right side:
\[ x = 1896 + 546 - 2431 = 11 \]

### Step 6: Calculate the mole percentage of \(^ {26}Mg\)
Since \(x\) represents the mole percentage of \(^ {25}Mg\):
\[ \text{Mole \% of } ^{25}Mg = 11\% \]
Thus, the mole percentage of \(^ {26}Mg\) is:
\[ 21 - x = 21 - 11 = 10\% \]

### Final Answer
The mole percentage of \(^ {26}Mg\) is **10%**.

---