This question is asking for the pH of a buffer solution between ammonia and nitric acid, with given volumes and concentrations. At the end, the result turns out to be 10.488.
<h3>Buffers</h3>
In chemistry, buffers are known as substances attempting to hold a relatively constant pH by mixing and acid and a base (weak and strong). In such a way, for the substances given, the first step will be to calculate the consumed moles as they are mixed:
![n_{NH_3}=0.1L*0.1mol/L=0.01mol\\\\n_{HNO_3}=0.09L*0.1mol/L=0.009mol](https://tex.z-dn.net/?f=n_%7BNH_3%7D%3D0.1L%2A0.1mol%2FL%3D0.01mol%5C%5C%5C%5Cn_%7BHNO_3%7D%3D0.09L%2A0.1mol%2FL%3D0.009mol)
Now, since ammonia is in a greater proportion, one can calculate how much of it is left after being consumed by the nitric acid:
![n_{NH_3}^{left}=0.01mol-0.009mol=0.001mol](https://tex.z-dn.net/?f=n_%7BNH_3%7D%5E%7Bleft%7D%3D0.01mol-0.009mol%3D0.001mol)
And its new concentration:
![[NH_3]=\frac{0.001mol}{0.1L+0.09L} =0.00526M](https://tex.z-dn.net/?f=%5BNH_3%5D%3D%5Cfrac%7B0.001mol%7D%7B0.1L%2B0.09L%7D%20%3D0.00526M)
Next, with ammonia's ionization:
![NH_3+H_2O\rightleftharpoons NH_4^++OH^-](https://tex.z-dn.net/?f=NH_3%2BH_2O%5Crightleftharpoons%20NH_4%5E%2B%2BOH%5E-)
We set up the equilibrium expression based on ammonia's Kb:
![Kb=\frac{[NH_4^+][OH^-]}{[NH_3]}](https://tex.z-dn.net/?f=Kb%3D%5Cfrac%7B%5BNH_4%5E%2B%5D%5BOH%5E-%5D%7D%7B%5BNH_3%5D%7D)
Which can be solved by introducing x and using ammonia's Kb:
![1.8x10^{-5}=\frac{x^2}{0.00526M}\\ \\](https://tex.z-dn.net/?f=1.8x10%5E%7B-5%7D%3D%5Cfrac%7Bx%5E2%7D%7B0.00526M%7D%5C%5C%20%5C%5C)
Then, we solve for x which is also equal to the concentration of ammonium and hydroxide ions in the solution:
![x=\sqrt{0.00526*1.8x10^{-5}}=0.000308M](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B0.00526%2A1.8x10%5E%7B-5%7D%7D%3D0.000308M)
Ultimately, we calculate the pOH and then turn it into pH with:
![pOH=-log(0.00308)=3.512\\\\pH=14-3.512=10.488](https://tex.z-dn.net/?f=pOH%3D-log%280.00308%29%3D3.512%5C%5C%5C%5CpH%3D14-3.512%3D10.488)
Learn more about buffers: brainly.com/question/24188850