Answer
47.60 g
Explanation
Given that:
Molar mass of MgCl₂ = 95.20 g/mol
Mass of Mg produced = 12.15 grams
Equation: MgCl₂ → Mg + Cl₂
What to find:
To calculate the grams of MgCl₂ needed to produce 12.15 grams of Mg.
Step-by-step solution:
Step 1: Convert the mass of Mg produced to moles.
Using the molar mass of Mg (24.305 g/mol) and the mole formula, the moles of Mg produced is
[tex]Moles=\frac{mass}{molar\text{ }mass}=\frac{12.15\text{ }g}{24.305\text{ }g\text{/}mol}=0.49989714\text{ }mol[/tex]Step 2: Determine the moles of MgCl₂ needed to produce 12.15 g of Mg.
According to the given equation; 1 mol of MgCl₂ produced 1 mol of Mg
So, x mol of MgCl₂ will produce 0.49989714 mol of Mg
That is:
[tex]\begin{gathered} 1mol\text{ }MgCl₂=1mol\text{ }Mg \\ \\ x=0.49989714mol\text{ }Mg \\ \\ x=\frac{0.49989714mol\text{ }Mg}{1mol\text{ }Mg}\times1mol\text{ }MgCl₂ \\ \\ x=0.49989714mol\text{ }MgCl₂ \end{gathered}[/tex]Step 3: Convert the moles of MgCl₂ needed to produce 12.15 g of Mg to grams.
Using the molar mass of MgCl₂ = 95.20 g/mol, therefore the mass in grams of MgCl₂ needed to produce 12.15 g of Mg will be:
[tex]\begin{gathered} Mass\text{ }of\text{ }MgCl_2\text{ }needed=Molar\text{ }mass\times Moles \\ \\ Mass\text{ }of\text{ }MgCl_2\text{ }needed=95.20\text{ }g\text{/}mol\times0.49989714\text{ }mol \\ \\ Mass\text{ }of\text{ }MgCl_2\text{ }needed=47.60\text{ }g \end{gathered}[/tex]Hence, the grams of MgCl₂ needed to produce 12.15 grams of Mg is 47.60 g.