Answer : The concentration of [tex]NH_4^+[/tex] ion is [tex]0.15E^1M[/tex]
Explanation :
First we have to calculate the moles of [tex](NH_4)_3PO_4[/tex].
[tex]\text{Moles of }(NH_4)_3PO_4=\text{Concentration of }(NH_4)_3PO_4\times \text{Volume of solution}=0.50M\times 0.06L=0.03mole[/tex]
The balanced chemical reaction will be:
[tex](NH_4)_3PO_4\rightleftharpoons 3NH_4^++PO_4^{3-}[/tex]
From the reaction we conclude that,
1 mole of [tex](NH_4)_3PO_4[/tex] dissociate to give 3 moles of [tex]NH_4^+[/tex] ion and 1 mole of [tex]PO_4^{3-}[/tex] ion
So,
0.03 mole of [tex](NH_4)_3PO_4[/tex] dissociate to give [tex]3\times 0.03=0.09[/tex] moles of [tex]NH_4^+[/tex] ion and 0.03 mole of [tex]PO_4^{3-}[/tex] ion
Now we have to calculate the concentration of [tex]NH_4^+[/tex] ion.
[tex]\text{Concentration of }NH_4^+=\frac{\text{Moles of }NH_4^+}{\text{Total volume}}[/tex]
[tex]\text{Concentration of }NH_4^+=\frac{0.09mole}{0.06L}=1.5M=0.15E^1M[/tex]
Therefore, the concentration of [tex]NH_4^+[/tex] ion is [tex]0.15E^1M[/tex]