Let's tackle each part of your question step by step.
### Part (a): Balancing the Equation
The unbalanced chemical equation is:
[tex]\[ \text{MgCl}_2 + \text{Fe} \rightarrow \text{Mg} + \text{FeCl}_3 \][/tex]
To balance this equation, let's ensure that we have the same number of each type of atom on both sides of the equation.
1. Start by looking at the magnesium atoms (Mg):
- On the left side, we have 1 Mg in MgCl₂.
- On the right side, we have 1 Mg.
So, the Mg atoms are already balanced.
2. Next, look at the chlorine atoms (Cl):
- On the left side, we have 2 Cl atoms in MgCl₂.
- On the right side, we have 3 Cl atoms in FeCl₃.
To balance Cl atoms, we need a multiple of 6 because it's the least common multiple of 2 and 3. Let's balance it by putting coefficients:
[tex]\( 3 \text{MgCl}_2 + \text{Fe} \rightarrow 3 \text{Mg} + 2 \text{FeCl}_3 \)[/tex]
3. Now, let's look at the iron atoms (Fe):
- On the left side, we have 2 Fe.
- On the right side, the balanced equation now has 2 Fe in 2 FeCl₃.
To balance Fe atoms:
[tex]\( 3 \text{MgCl}_2 + 2 \text{Fe} \rightarrow 3 \text{Mg} + 2 \text{FeCl}_3 \)[/tex]
So, the balanced equation is:
[tex]\[ 3 \text{MgCl}_2 + 2 \text{Fe} \rightarrow 3 \text{Mg} + 2 \text{FeCl}_3 \][/tex]
### Part (b): Calculating the Grams of FeCl₃ Produced from 571.8 grams of MgCl₂
1. Calculate the molar masses:
- MgCl₂: Magnesium (Mg) has a molar mass of 24.305 g/mol, and Chlorine (Cl) has a molar mass of 35.453 g/mol each. Therefore, the molar mass of MgCl₂ is:
[tex]\[
24.305 + (2 \times 35.453) = 24.305 + 70.906 = 95.211 \text{ g/mol}
\][/tex]
- FeCl₃: Iron (Fe) has a molar mass of 55.845 g/mol, and Chlorine (Cl) has a molar mass of 35.453 g/mol each. Therefore, the molar mass of FeCl₃ is:
[tex]\[
55.845 + (3 \times 35.453) = 55.845 + 106.359 = 162.204 \text{ g/mol}
\][/tex]
2. Calculate the moles of MgCl₂:
- Given 571.8 grams of MgCl₂, and knowing its molar mass:
[tex]\[
\text{Moles of MgCl}_2 = \frac{571.8 \text{ grams}}{95.211 \text{ g/mol}} \approx 6.0056 \text{ moles}
\][/tex]
3. Use the stoichiometry of the balanced equation:
- According to the balanced equation, 3 moles of MgCl₂ produce 2 moles of FeCl₃. Therefore:
[tex]\[
\text{Moles of FeCl}_3 = \left( \frac{2}{3} \right) \times 6.0056 \approx 4.0037 \text{ moles}
\][/tex]
4. Convert moles of FeCl₃ to grams:
- Knowing the molar mass of FeCl₃:
[tex]\[
\text{Mass of FeCl}_3 = 4.0037 \text{ moles} \times 162.204 \text{ g/mol} \approx 649.4225 \text{ grams}
\][/tex]
Therefore, from 571.8 grams of MgCl₂, you can produce approximately 649.42 grams of FeCl₃.
