To find the number of moles of ammonium \( \text{NH}_4^+ \) at equilibrium, we can use the concentration and the volume of the solution.
Given:
- The equilibrium concentration of \( \text{NH}_4^+ \) is \( 0.2 , M \).
- The volume of the solution is \( 100 , \text{ml} + 50 , \text{ml} = 150 , \text{ml} \) or \( 0.150 , \text{L} \).
To calculate the moles of \( \text{NH}_4^+ \) at equilibrium, use the formula:
\[ \text{Moles} = \text{Concentration} \times \text{Volume} \]
Substituting the known values:
\[ \text{Moles of } \text{NH}_4^+ = 0.2 , \text{mol/L} \times 0.150 , \text{L} = 0.03 , \text{moles} \]
Therefore, the number of moles of ammonium \( \text{NH}_4^+ \) at equilibrium is 0.03 moles.