Answer : The mass of [tex]MgBr_2[/tex] needed to produce are, 1150 grams
Solution : Given,
Mass of metal (magnesium) = 75 g
Molar mass of magnesium = 24 g/mole
Molar mass of [tex]MgBr_2[/tex] = 184 g/mole
First we have to calculate the moles of metal (magnesium).
[tex]\text{Moles of Mg}=\frac{\text{Mass of Mg}}{\text{Molar mass of Mg}}=\frac{75g}{24g/mole}=6.25moles[/tex]
Now we have to calculate the moles of [tex]MgBr_2[/tex].
The balanced chemical reaction will be,
[tex]Mg+Br_2\rightarrow MgBr_2[/tex]
From the balanced reaction we conclude that
1 moles of magnesium react to give 1 mole of [tex]MgBr_2[/tex]
6.25 moles of magnesium react to give 6.25 moles of [tex]MgBr_2[/tex]
Now we have to calculate the mass of [tex]MgBr_2[/tex]
[tex]\text{Mass of }MgBr_2=\text{Moles of }MgBr_2\times \text{Molar mass of }MgBr_2[/tex]
[tex]\text{Mass of }MgBr_2=(6.25mole)\times (184g/mole)=1150g[/tex]
Therefore, the mass of [tex]MgBr_2[/tex] needed to produce are, 1150 grams