Questions: Balance the following equation with the smallest whole number coefficients. When balanced, what is the coefficient for B (in the reactants)? Sc2O3 + ... B → ScB2 + ... BO a) 1 b) 3 c) 5 d) 7 e) 9

Balance the following equation with the smallest whole number coefficients. When balanced, what is the coefficient for B (in the reactants)?
Sc2O3 + ... B → ScB2 + ... BO
a) 1
b) 3
c) 5
d) 7
e) 9

Transcript text: Balance the following equation with the smallest whole number coefficients. When balanced, what is the coefficient for B (in the reactants)? \[ { }_{-} \mathrm{Sc}_{2} \mathrm{O}_{3}+\ldots \mathrm{B} \rightarrow \_\mathrm{ScB}_{2}+\ldots \mathrm{BO} \] a) 1 b) 3 c) 5 d) 7 e) 9

Solution

Solution Steps

Step 1: Write the Unbalanced Equation

The unbalanced chemical equation is:

\[ \mathrm{Sc}_2\mathrm{O}_3 + x\mathrm{B} \rightarrow y\mathrm{ScB}_2 + z\mathrm{BO} \]

Step 2: Balance Scandium (Sc)

There are 2 scandium atoms on the left side in \(\mathrm{Sc}_2\mathrm{O}_3\). To balance scandium, we need 2 \(\mathrm{ScB}_2\) on the right side:

\[ \mathrm{Sc}_2\mathrm{O}_3 + x\mathrm{B} \rightarrow 2\mathrm{ScB}_2 + z\mathrm{BO} \]

Step 3: Balance Boron (B)

Each \(\mathrm{ScB}_2\) contains 2 boron atoms, and there are 2 \(\mathrm{ScB}_2\) on the right side, giving a total of \(2 \times 2 = 4\) boron atoms. Additionally, there are \(z\) boron atoms in \(\mathrm{BO}\). Therefore, the total number of boron atoms on the right side is \(4 + z\).

To balance boron, we set the number of boron atoms on the left side equal to the number on the right side:

\[ x = 4 + z \]

Step 4: Balance Oxygen (O)

There are 3 oxygen atoms on the left side in \(\mathrm{Sc}_2\mathrm{O}_3\). Each \(\mathrm{BO}\) contains 1 oxygen atom, so to balance oxygen, we need:

\[ z = 3 \]

Step 5: Solve for Boron Coefficient

Substitute \(z = 3\) into the boron balance equation:

\[ x = 4 + 3 = 7 \]