ANSWER
The mass of the first product (calcium) in grams is 100.195 grams
EXPLANATION
Given that
The mass of calcium nitrate is 410.0 grams
Step 1; Write the balanced equation of the reaction
[tex]\text{ Ca\lparen NO}_3)_2\text{ }+\text{ 2Li }\rightarrow\text{ Ca}_{(s)\text{ }}\text{ }+\text{ 2LiNO}_3[/tex]In the above reaction, 1 mole of calcium nitrate reacts with 2 moles of Li to produce 1 mole of Ca and 2 moles of LiNO3
Step 2; Find the mole of calcium nitrate using the below formula
[tex]\text{ mole }=\text{ }\frac{\text{ mass}}{\text{ molar mass}}[/tex]Recall, that the molar mass of Ca(NO3)2 is 164.1 g/mol
[tex]\begin{gathered} \text{ mole }=\text{ }\frac{410}{164.1} \\ \text{ mole }=\text{ 2.50 moles} \end{gathered}[/tex]The moles of Calcium nitrate is 2.50 moles
Step 3; Find the mole of calcium using stoichiometry ratio
Since calcium is the first product of the reaction, hence, the number of moles of calcium can be calculated below
1 mole of Ca(NO3)2 produced 1 mole of ca
Let the number of moles of calcium be x
[tex]\begin{gathered} \text{ 1 mole Ca\lparen NO}_3)_2\text{ }\rightarrow\text{ 1 mole Ca} \\ \text{ 2.5 moles Ca\lparen NO}_3)_2\text{ }\rightarrow\text{ x mole Ca} \\ \text{ cross multiply} \\ \text{ x mole Ca }\times\text{ 1 mole Ca\lparen NO}_3)_2\text{ }=\text{ 1 mole Ca}\times\text{ 2.5 moles Ca\lparen NO}_3)_2 \\ \text{ Isolate x mole Ca} \\ \text{ x mole Ca }=\text{ }\frac{1\text{ mole Ca}\times2.5\cancel{moles\text{ Ca\lparen NO}_3})_2}{1\cancel{mole\text{ Ca\lparen NO}_3})_2} \\ \text{ x mole Ca }=\text{ }\frac{1\text{ }\times\text{ 2.5 }}{1} \\ \text{ x }=\text{ 2.5 moles} \end{gathered}[/tex]Therefore, the number of moles of calcium is 2.5 moles
Step 4; Find the mass of Ca using the below formula
[tex]\text{ mole }=\text{ }\frac{\text{ mass}}{\text{ molar mass}}[/tex]recall, that the molar mass of calcium is 40.078 g/mol
[tex]\begin{gathered} \text{ 2.5 }=\text{ }\frac{\text{ mass}}{\text{ 40.087}} \\ \text{ cross multiply} \\ \text{ mass }=\text{ 2.5 }\times\text{ 40.078} \\ \text{ mass }=\text{ 100.195 grams} \end{gathered}[/tex]Therefore, the mass of the first product (calcium) in grams is 100.195 grams
