If mass of 5 mole `AB_(2)` is `125xx10^(-3)kg` and mass of 10 mole `A_(2)B_(2)` is `300xx10^(-3)kg`. Then correct molar mass of A and B respectively (in kg/mol):

Options

A. `A=5xx10^(-3)&B=25xx10^(-3)`
B. `A=2.5xx10^(-3)&B=5xx10^(-3)`
C. `A=2.5xx10^(-3)&B=10xx10`
D. `A=5xx10^(-3)&B=10xx10^(-3)`

Answer

To solve the problem, we need to find the molar masses of elements A and B based on the given information about the compounds \( AB_2 \) and \( A_2B_2 \).

### Step-by-step Solution:

1. **Calculate the molar mass of \( AB_2 \)**:
- We know that the mass of 5 moles of \( AB_2 \) is \( 125 \times 10^{-3} \) kg.
- To find the mass of 1 mole of \( AB_2 \):
\[ \text{Mass of 1 mole of } AB_2 = \frac{125 \times 10^{-3} \text{ kg}}{5} = 25 \times 10^{-3} \text{ kg} \]

2. **Express the mass of \( AB_2 \) in terms of A and B**:
- The formula \( AB_2 \) consists of 1 mole of A and 2 moles of B.
- Let the molar mass of A be \( M_A \) (kg/mol) and the molar mass of B be \( M_B \) (kg/mol).
- Therefore, the mass of 1 mole of \( AB_2 \) can be expressed as:
\[ M_A + 2M_B = 25 \times 10^{-3} \text{ kg} \quad \text{(Equation 1)} \]

3. **Calculate the molar mass of \( A_2B_2 \)**:
- We know that the mass of 10 moles of \( A_2B_2 \) is \( 300 \times 10^{-3} \) kg.
- To find the mass of 1 mole of \( A_2B_2 \):
\[ \text{Mass of 1 mole of } A_2B_2 = \frac{300 \times 10^{-3} \text{ kg}}{10} = 30 \times 10^{-3} \text{ kg} \]

4. **Express the mass of \( A_2B_2 \) in terms of A and B**:
- The formula \( A_2B_2 \) consists of 2 moles of A and 2 moles of B.
- Therefore, the mass of 1 mole of \( A_2B_2 \) can be expressed as:
\[ 2M_A + 2M_B = 30 \times 10^{-3} \text{ kg} \quad \text{(Equation 2)} \]

5. **Simplify Equation 2**:
- Dividing Equation 2 by 2 gives:
\[ M_A + M_B = 15 \times 10^{-3} \text{ kg} \quad \text{(Equation 3)} \]

6. **Solve the system of equations**:
- We now have two equations:
- Equation 1: \( M_A + 2M_B = 25 \times 10^{-3} \)
- Equation 3: \( M_A + M_B = 15 \times 10^{-3} \)
- Subtract Equation 3 from Equation 1:
\[ (M_A + 2M_B) - (M_A + M_B) = 25 \times 10^{-3} - 15 \times 10^{-3} \]
\[ M_B = 10 \times 10^{-3} \text{ kg/mol} \]

7. **Substitute \( M_B \) back to find \( M_A \)**:
- Substitute \( M_B \) into Equation 3:
\[ M_A + 10 \times 10^{-3} = 15 \times 10^{-3} \]
\[ M_A = 15 \times 10^{-3} - 10 \times 10^{-3} = 5 \times 10^{-3} \text{ kg/mol} \]

### Final Answer:
- The molar mass of A is \( 5 \times 10^{-3} \) kg/mol.
- The molar mass of B is \( 10 \times 10^{-3} \) kg/mol.