Molecular mass of phosphate of divalent metal is 262. Find the atomic mass of the metal.

Explanation

To find the atomic mass of the divalent metal in the phosphate compound with a total molecular mass of 262, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Phosphate Ion**:
The phosphate ion is represented as \( PO_4^{3-} \). This means it has one phosphorus atom and four oxygen atoms.

2. **Determine the Formula of the Metal Phosphate**:
Since the metal is divalent (has a charge of +2), we can use the criss-cross method to find the formula of the metal phosphate. The charges will combine to give us:
- The metal (M) has a charge of +2.
- The phosphate (PO4) has a charge of -3.
Thus, the formula for the metal phosphate will be \( M_3(PO_4)_2 \).

3. **Calculate the Molecular Mass of the Metal Phosphate**:
The molecular mass is given as 262. We can express the molecular mass in terms of the atomic mass of the metal (let's denote it as \( A \)):
\[ \text{Molecular mass} = 3A + 2(\text{mass of P}) + 8(\text{mass of O}) \]
The atomic mass of phosphorus (P) is 31 and that of oxygen (O) is 16.

4. **Substituting Known Values**:
Substitute the known values into the equation:
\[ 262 = 3A + 2(31) + 8(16) \]
Calculate the contributions from phosphorus and oxygen:
\[ 2(31) = 62 \quad \text{and} \quad 8(16) = 128 \]
Therefore, the equation becomes:
\[ 262 = 3A + 62 + 128 \]

5. **Simplifying the Equation**:
Combine the constants:
\[ 262 = 3A + 190 \]
Now, isolate \( 3A \):
\[ 3A = 262 - 190 \]
\[ 3A = 72 \]

6. **Solving for A**:
Divide both sides by 3 to find \( A \):
\[ A = \frac{72}{3} = 24 \]

7. **Conclusion**:
The atomic mass of the divalent metal is \( 24 \).