Answer : The mass of sodium iodide used to produced must be, 105.22 grams.
Explanation : Given,
Mass of [tex]I_2[/tex] = 89.1 g
Molar mass of [tex]I_2[/tex] = 253.8 g/mole
Molar mass of [tex]NaI[/tex] = 149.89 g/mole
First we have to calculate the moles of [tex]I_2[/tex].
[tex]\text{Moles of }I_2=\frac{\text{Mass of }I_2}{\text{Molar mass of }I_2}=\frac{89.1g}{253.8g/mole}=0.351moles[/tex]
Now we have to calculate the moles of [tex]NaI[/tex].
The balanced chemical reaction is,
[tex]2NaI(aq)+Cl_2(g)\rightarrow I_2(s)+2NaCl(aq)[/tex]
From the balanced chemical reaction, we conclude that
As, 1 mole of [tex]I_2[/tex] obtained from 2 moles of [tex]NaI[/tex]
So, 0.351 moles of [tex]I_2[/tex] obtained from [tex]2\times 0.351=0.702[/tex] moles of [tex]NaI[/tex]
Now we have to calculate the mass of [tex]NaI[/tex].
[tex]\text{Mass of }NaI=\text{Moles of }NaI\times \text{Molar mass of }NaI[/tex]
[tex]\text{Mass of }NaI=(0.702mole)\times (149.89g/mole)=105.22g[/tex]
Therefore, the mass of sodium iodide used to produced must be, 105.22 grams.