Question

part a
when the equation no₂ + h₂o + o₂ → hno₃ is balanced, the coefficient of hno₃ is:
3
4
2
5
none of the above

Explanation:

Step1: Balance N atoms

Let the coefficients be \( a\,\text{NO}_2 + b\,\text{H}_2\text{O} + c\,\text{O}_2
ightarrow d\,\text{HNO}_3 \).
For N: \( a = d \).

Step2: Balance H atoms

For H: \( 2b = d \) (since \( \text{H}_2\text{O} \) has 2 H, \( \text{HNO}_3 \) has 1 H).

Step3: Balance O atoms

Left O: \( 2a + b + 2c \) (from \( \text{NO}_2 \), \( \text{H}_2\text{O} \), \( \text{O}_2 \)).
Right O: \( 3d \) (from \( \text{HNO}_3 \)).

Substitute \( a = d \) and \( b = \frac{d}{2} \) into O balance:
\( 2d + \frac{d}{2} + 2c = 3d \)
Simplify: \( \frac{5d}{2} + 2c = 3d \) → \( 2c = \frac{d}{2} \) → \( c = \frac{d}{4} \).

To eliminate fractions, let \( d = 4 \). Then:
\( a = 4 \), \( b = 2 \), \( c = 1 \).

Check equation: \( 4\text{NO}_2 + 2\text{H}_2\text{O} + 1\text{O}_2
ightarrow 4\text{HNO}_3 \).
N: 4=4, H: 4=4, O: \( 8 + 2 + 2 = 12 \) (left), \( 12 \) (right). Balanced.

Answer:

4 (corresponding to the option "4")