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This is a titration problem-  -not not necessarily a buffer problem. While you have .0055$0.0055$ moles of NH3$\ce{NH3}$, you have .01$0.01$ moles of H$\ce{H}$ from HCl$\ce{HCl}$ dissociating. .01-.0055=.0045$0.01 - 0.0055 = 0.0045$ moles of H$\ce{H}$ left. Take H/total L to find M. Take the -log$-\log$ of [H]$\ce{[H]}$.

This is a titration problem--not necessarily a buffer problem. While you have .0055 moles of NH3, you have .01 moles of H from HCl dissociating. .01-.0055=.0045 moles of H left. Take H/total L to find M. Take the -log of [H].

This is a titration problem  - not necessarily a buffer problem. While you have $0.0055$ moles of $\ce{NH3}$, you have $0.01$ moles of $\ce{H}$ from $\ce{HCl}$ dissociating. $0.01 - 0.0055 = 0.0045$ moles of $\ce{H}$ left. Take H/total L to find M. Take the $-\log$ of $\ce{[H]}$.

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This is a titration problem--not necessarily a buffer problem. While you have .0055 moles of NH3, you have .01 moles of H from HCl dissociating. .01-.0055=.0045 moles of H left. Take H/total L to find M. Take the -log of [H].