# Question 853bc

Dec 11, 2014

The answer is $0.12 g$.

Essentially, what you are dealing with is a double replacement precipitation reaction in which two soluble ionic compounds (two soluble salts) react to form an insoluble precipitate.

Starting from the balanced chemical equation, we get

$N a C {l}_{\left(a q\right)} + A g N {O}_{3 \left(a q\right)} \to N a N {O}_{3 \left(a q\right)} + A g C {l}_{\left(s\right)}$

The complete ionic equation, which better describes the reaction since ionic compounds dissociate into ions when dissolved in water, is

$A {g}_{\left(a q\right)}^{+} + N {O}_{3 \left(a q\right)}^{-} + N {a}_{\left(a q\right)}^{+} + C {l}_{\left(a q\right)}^{-} \to A g C {l}_{\left(s\right)} + N {a}_{\left(a q\right)}^{+} + N {O}_{3 \left(a q\right)}^{-}$

Notice that $N {a}_{\left(a q\right)}^{+}$ and $N {O}_{3 \left(a q\right)}^{-}$ did not participate in the reaction since they can be found on both sides of the equation -> such ions are called spectator ions.

This gives us the net ionic equation, which shows us what ions participate in the reaction that forms the precipitate

$A {g}_{\left(a q\right)}^{+} + C {l}_{\left(a q\right)}^{-} \to A g C {l}_{\left(s\right)}$

Now, we know that we have a $1 : 1$ mole ratio for $N a C l$ and $A g N {O}_{3}$; the number of moles of $A g N {O}_{3}$ can be determined from molarity, C = n_(solute)/(V_(solution)#

${n}_{s o l u t e} = C \cdot {V}_{s o l u t i o n} = \frac{0.100 m o l e s}{L} \cdot \left(20 \cdot {10}^{- 3}\right) L$ = 0.0020 moles

This means that the number of moles of $N a C l$ must be 0.0020 as well. Knowing $N a C l$'s molar mass - $58.5 \frac{g}{m o l}$ - we get

${m}_{N a C l} = 0.0020 m o l e s \cdot 58.5 \frac{g}{m o l} = 0.12 g$

This is true because the number of moles of $N a C l$ dissociate into moles of $N {a}^{+}$ and moles of $C {l}^{-}$, the same being true for $A g N {O}_{3}$; therefore, the number of $N a C l$ moles must be at least equat to the number of $A g N {O}_{3}$ moles.

A more in depth analysis could be done using the concentrations of the compounds, the reaction's coefficient (${Q}_{s p}$), and ${K}_{s p}$.

Here's a video of the reaction: