Answer : The pH of the solution is, 5.24
Explanation :
First we have to calculate the volume of ![HNO_3](https://tex.z-dn.net/?f=HNO_3)
Formula used :
![M_1V_1=M_2V_2](https://tex.z-dn.net/?f=M_1V_1%3DM_2V_2)
where,
are the initial molarity and volume of
.
are the final molarity and volume of
.
We are given:
![M_1=0.3403M\\V_1=160.0mL\\M_2=0.0501M\\V_2=?](https://tex.z-dn.net/?f=M_1%3D0.3403M%5C%5CV_1%3D160.0mL%5C%5CM_2%3D0.0501M%5C%5CV_2%3D%3F)
Putting values in above equation, we get:
![0.3403M\times 160.0mL=0.0501M\times V_2\\\\V_2=1086.79mL](https://tex.z-dn.net/?f=0.3403M%5Ctimes%20160.0mL%3D0.0501M%5Ctimes%20V_2%5C%5C%5C%5CV_2%3D1086.79mL)
Now we have to calculate the total volume of solution.
Total volume of solution = Volume of
+ Volume of ![HNO_3](https://tex.z-dn.net/?f=HNO_3)
Total volume of solution = 160.0 mL + 1086.79 mL
Total volume of solution = 1246.79 mL
Now we have to calculate the Concentration of salt.
![\text{Concentration of salt}=\frac{0.3403M}{1246.79mL}\times 160.0mL=0.0437M](https://tex.z-dn.net/?f=%5Ctext%7BConcentration%20of%20salt%7D%3D%5Cfrac%7B0.3403M%7D%7B1246.79mL%7D%5Ctimes%20160.0mL%3D0.0437M)
Now we have to calculate the pH of the solution.
At equivalence point,
![pOH=\frac{1}{2}[pK_w+pK_b+\log C]](https://tex.z-dn.net/?f=pOH%3D%5Cfrac%7B1%7D%7B2%7D%5BpK_w%2BpK_b%2B%5Clog%20C%5D)
![pOH=\frac{1}{2}[14+4.87+\log (0.0437)]](https://tex.z-dn.net/?f=pOH%3D%5Cfrac%7B1%7D%7B2%7D%5B14%2B4.87%2B%5Clog%20%280.0437%29%5D)
![pOH=8.76](https://tex.z-dn.net/?f=pOH%3D8.76)
![pH+pOH=14\\\\pH=14-pOH\\\\pH=14-8.76\\\\pH=5.24](https://tex.z-dn.net/?f=pH%2BpOH%3D14%5C%5C%5C%5CpH%3D14-pOH%5C%5C%5C%5CpH%3D14-8.76%5C%5C%5C%5CpH%3D5.24)
Thus, the pH of the solution is, 5.24