Question

Calculate how many grams of MgCl2 are needed to produce 12.15 grams

Answer 1

47.60 g

Step-by-step 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

`Moles=\frac{mass}{molar\text{ }mass}=\frac{12.15\text{ }g}{24.305\text{ }g\text{/}mol}=0.49989714\text{ }mol`

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:

`\begin{gathered} 1mol\text{ }MgCl₂=1mol\text{ }Mg \\ \\ x=0.49989714mol\text{ }Mg \\ \\ x=\frac{0.49989714mol\text{ }Mg}{1mol\text{ }Mg}*1mol\text{ }MgCl₂ \\ \\ x=0.49989714mol\text{ }MgCl₂ \end{gathered}`

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:

`\begin{gathered} Mass\text{ }of\text{ }MgCl_2\text{ }needed=Molar\text{ }mass* Moles \\ \\ Mass\text{ }of\text{ }MgCl_2\text{ }needed=95.20\text{ }g\text{/}mol*0.49989714\text{ }mol \\ \\ Mass\text{ }of\text{ }MgCl_2\text{ }needed=47.60\text{ }g \end{gathered}`

Hence, the grams of MgCl₂ needed to produce 12.15 grams of Mg is 47.60 g.