Answer
$$K = 3.4$$
Work Step by Step
- The exponent of each concentration is equal to its balance coefficient.
$$K = \frac{[Products]}{[Reactants]} = \frac{[ SO_3 ][ NO ]}{[ SO_2 ][ NO_2 ]}$$
1. Draw the ICE table for this equilibrium:
$$\begin{vmatrix}
Compound& [ SO_2 ]& [ NO_2 ]& [ SO_3 ]& [ NO ]\\
Initial& 2.00 & 2.00 & 0 & 0 \\
Change& -x& -x& +x& +x\\
Equilibrium& 2.00 -x& 2.00 -x& 0 +x& 0 +x\\
\end{vmatrix}$$
2. At equilibrium, these are the concentrations of each compound:
$ [ SO_2 ] = 2.00 \space M - x$
$ [ NO_2 ] = 2.00 \space M - x$
$ [ SO_3 ] = 0 \space M + x$
$ [ NO ] = 0 \space M + x$
3. Using the concentration of $ NO $ at equilibrium, find x:
$ 0 + x = 1.30 $
$ x = 1.30 - 0 $
$x = 1.30 $
$ [ SO_2 ] = 2.00 \space M - 1.30 =0.700 $
$ [ NO_2 ] = 2.00 \space M - 1.30 =0.700 $
$ [ SO_3 ] = 0 \space M + 1.30 =1.30 $
$ [ NO ] = 0 \space M + 1.30 =1.30 $
- The exponent of each concentration is equal to its balance coefficient.
$$K = \frac{[Products]}{[Reactants]} = \frac{[ SO_3 ][ NO ]}{[ SO_2 ][ NO_2 ]}$$
4. Substitute the values and calculate the constant value:
$$K = \frac{( 1.30 )( 1.30 )}{( 0.700 )( 0.700 )} = 3.4$$