Answer:
2
Step-by-step explanation:
You want the coefficient of silver iodide in the equation ...
_AgI +_Na₂S ⇒ _Ag₂S +_NaI
Balanced equation
The equation is balanced when the numbers of each of the species is the same on each side of the equation.
We can write four equations in the four unknowns to find the coefficients, or we can use a little guesswork.
If we suppose the coefficient of silver sulfide (Ag₂S) is 1, that tells us the coefficient of silver iodide (AgI) will be 2. If that is the case, then there are two atoms of iodine that will make the coefficient of NaI be 2. This is consistent with the coefficient of Na₂S being 1, giving one Sulfur atom on each side of the equation.
The balanced equation is ...
2AgI +Na₂S ⇒ Ag₂S +2NaI
The coefficient of silver iodide is 2.
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Additional comment
If the reaction is ...
a·AgI + b·Na₂S ⇒ c·Ag₂S + d·NaI
We can write the relationships between the coefficients as follows. This ultimately gives rise to 3 equations in 4 unknowns, so the choice of any given coefficient is arbitrary. We choose to use the smallest integers that satisfy the conditions.
The balance for Ag is ...
a = 2c
The balance for I is ...
a = d
The balance for Na is ...
2b = d
The balance for S is ...
b = c
Then, in terms of 'a' and 'b', we have ...
a = d = 2b = 2c
For b = c = 1, a = d = 2, as we determined above.