Question

_S8+_O2 = _SO3
Find the coefficients to make both sides equal

Answer 1

To balance the chemical equation \( S_8 + O_2 \rightarrow SO_3 \), we need to ensure that the number of each type of atom is equal on both sides.

1. Start with \( S_8 \) and \( O_2 \) on the left.
2. The product is \( SO_3 \).

Let’s assign coefficients to each compound:

- Let \( a \) be the coefficient for \( S_8 \).
- Let \( b \) be the coefficient for \( O_2 \).
- Let \( c \) be the coefficient for \( SO_3 \).

The unbalanced equation can be rewritten as:

\[ a S_8 + b O_2 \rightarrow c SO_3 \]

From the left side, we have:
- \( 8a \) sulfur atoms (from \( S_8 \))
- \( 2b \) oxygen atoms (from \( O_2 \))

From the right side, we have:
- \( c \) sulfur atoms (from \( SO_3 \))
- \( 3c \) oxygen atoms (from \( SO_3 \))

Setting up the equations for balance:

1. For sulfur:
\[
8a = c
\]

2. For oxygen:
\[
2b = 3c
\]

Now, we start with \( a = 1 \) (which means we have 1 molecule of \( S_8 \)):
\[
c = 8a = 8(1) = 8
\]

Now, substitute \( c \) into the oxygen equation:
\[
2b = 3(8) \implies 2b = 24 \implies b = 12
\]

So the coefficients are:
- \( a = 1 \) (for \( S_8 \))
- \( b = 12 \) (for \( O_2 \))
- \( c = 8 \) (for \( SO_3 \))

Putting this all together, the balanced equation is:
\[
1 S_8 + 12 O_2 \rightarrow 8 SO_3
\]

The coefficients to make both sides equal are:
\[ 1, 12, 8 \]

Thus, the balanced equation is:

\[
S_8 + 12 O_2 \rightarrow 8 SO_3
\]