Question

Consider the following chemical equation:
\(p \, \text{MnO}_2 + q \, \text{Al} \rightarrow r \, \text{Mn} + s \, \text{Al}_2\text{O}_3\)
To balance this chemical equation, the values of the coefficients \(p\), \(q\), \(r\), and \(s\) must be respectively:

• A. 3, 2, 3, 4
• B. 4, 3, 4, 2
• C. 3, 4, 3, 2
• D. 4, 2, 4, 3

Answer 1

The Correct Option is C

To balance the chemical equation, we need to ensure that the number of atoms of each element is the same on both sides of the equation. Let’s balance the equation systematically:

We can start by balancing the manganese (\(\text{Mn}\)) atoms: \(p = r\)

Next, let’s balance the aluminum (\(\text{Al}\)) atoms: \(q = 2s\)

Finally, let’s balance the oxygen (\(\text{O}\)) atoms: \(2p = 3s\)
Now we have a system of three equations with four unknowns:

\[ p = r \\ q = 2s \\ 2p = 3s \]

Let’s test the given options:

• (A) 3, 2, 3, 4: Does not balance (oxygen is unbalanced)
• (B) 4, 3, 4, 2: Does not balance (oxygen is unbalanced)
• (C) 3, 4, 3, 2: This gives: \(3\text{MnO}_2 + 4\text{Al} \rightarrow 3\text{Mn} + 2\text{Al}_2\text{O}_3\). This is balanced.
• (D) 4, 2, 4, 3: Does not balance (aluminum is unbalanced).

Therefore, the correct coefficients are \(3, 4, 3, 2\), as shown in option (C).