How many moles of potassium are needed to react completely with 12.8 moles of magnesium bromide according to this balanced chemical equation?

[tex]\( 2 K + MgBr_2 \rightarrow Mg + 2 KBr \)[/tex]

A. 12.8 moles [tex]\(K\)[/tex]
B. 25.6 moles [tex]\(K\)[/tex]
C. 6.40 moles [tex]\(K\)[/tex]
D. 51.2 moles [tex]\(K\)[/tex]



Answer :

To determine how many moles of potassium (K) are needed to react completely with 12.8 moles of magnesium bromide (MgBr[tex]\(_2\)[/tex]) according to the balanced chemical equation, let’s follow these steps:

1. Write down the balanced chemical equation:
[tex]\[ 2 K + MgBr_2 \rightarrow Mg + 2 KBr \][/tex]

2. Identify the mole ratio of potassium (K) to magnesium bromide (MgBr[tex]\(_2\)[/tex]) from the balanced equation. According to the equation:
[tex]\[ 2 \text{ moles of } K \text{ react with } 1 \text{ mole of } MgBr_2 \][/tex]

3. We are given that we have 12.8 moles of MgBr[tex]\(_2\)[/tex]. Using the mole ratio from the balanced equation, we need to calculate how many moles of K are required to react with 12.8 moles of MgBr[tex]\(_2\)[/tex].

4. Multiply the number of moles of MgBr[tex]\(_2\)[/tex] by the mole ratio of K to MgBr[tex]\(_2\)[/tex]:
[tex]\[ \text{moles of } K \text{ needed} = 12.8 \text{ moles of } MgBr_2 \times \left(\frac{2 \text{ moles of } K}{1 \text{ mole of } MgBr_2}\right) \][/tex]

5. Perform the multiplication:
[tex]\[ \text{moles of } K \text{ needed} = 12.8 \times 2 = 25.6 \text{ moles of } K \][/tex]

So, the number of moles of potassium required to react completely with 12.8 moles of magnesium bromide is [tex]\(25.6\)[/tex] moles of [tex]\(K\)[/tex].

Thus, the correct answer is:
[tex]\[ \boxed{25.6 \text{ moles of } K} \][/tex]