5 moles of `AB_(2)` weigh `125 xx 10^(-3)` kg and 10 moles of `A_(2)B_(2)` weigh `300 xx 10^(-3)` kg. What is the sum of molar mass of A `(M_(A))` and molar mass of `B(M_(B))` in `g "mol"^(-1)` ?

Explanation

To solve the problem, we need to find the sum of the molar masses of elements A and B based on the given information about the compounds AB₂ and A₂B₂.

### Step-by-Step Solution:

1. **Convert the Masses from kg to g:**
- For AB₂:
\[ \text{Mass of } AB_2 = 125 \times 10^{-3} \text{ kg} = 125 \text{ g} \]
- For A₂B₂:
\[ \text{Mass of } A_2B_2 = 300 \times 10^{-3} \text{ kg} = 300 \text{ g} \]

2. **Calculate the Molar Mass of AB₂:**
- We know that 5 moles of AB₂ weigh 125 g. Therefore, the molar mass of AB₂ can be calculated as:
\[ \text{Molar mass of } AB_2 = \frac{\text{Mass}}{\text{Moles}} = \frac{125 \text{ g}}{5 \text{ moles}} = 25 \text{ g/mol} \]

3. **Calculate the Molar Mass of A₂B₂:**
- We know that 10 moles of A₂B₂ weigh 300 g. Therefore, the molar mass of A₂B₂ can be calculated as:
\[ \text{Molar mass of } A_2B_2 = \frac{\text{Mass}}{\text{Moles}} = \frac{300 \text{ g}}{10 \text{ moles}} = 30 \text{ g/mol} \]

4. **Set Up the Molar Mass Relationships:**
- The molar mass of AB₂ can be expressed in terms of the molar masses of A and B:
\[ M_A + 2M_B = 25 \text{ g/mol} \quad \text{(1)} \]
- The molar mass of A₂B₂ can be expressed similarly:
\[ 2M_A + 2M_B = 30 \text{ g/mol} \quad \text{(2)} \]

5. **Simplify Equation (2):**
- Dividing equation (2) by 2 gives:
\[ M_A + M_B = 15 \text{ g/mol} \quad \text{(3)} \]

6. **Solve the System of Equations:**
- Now we have two equations:
- From (1): \( M_A + 2M_B = 25 \)
- From (3): \( M_A + M_B = 15 \)
- Subtract (3) from (1):
\[ (M_A + 2M_B) - (M_A + M_B) = 25 - 15 \]
\[ M_B = 10 \text{ g/mol} \]

7. **Substitute to Find Molar Mass of A:**
- Substitute \( M_B \) back into equation (3):
\[ M_A + 10 = 15 \]
\[ M_A = 5 \text{ g/mol} \]

8. **Calculate the Sum of Molar Masses:**
- Finally, we find the sum of the molar masses of A and B:
\[ M_A + M_B = 5 \text{ g/mol} + 10 \text{ g/mol} = 15 \text{ g/mol} \]

### Final Answer:
The sum of the molar mass of A and the molar mass of B is **15 g/mol**.