Answer
$$K_C = 4.0 \times 10^{8}$$
Work Step by Step
- Calculate all the concentrations:
$$[N_2] = ( 2.80 x 10^{-4} )/(2.00) = 1.40 x 10^{-4} M$$
$$[O_2] = ( 2.50 x 10^{-5} )/(2.00) = 1.25 x 10^{-5} M$$
$$[N_2O] = ( 2.00 x 10^{-2} )/(2.00) = 1.00 x 10^{-2} M$$
- The exponent of each concentration is equal to its balance coefficient.
$$K_C = \frac{[Products]}{[Reactants]} = \frac{[ N_2O ] ^{ 2 }}{[ N_2 ] ^{ 2 }[ O_2 ]}$$
2. Substitute the values and calculate the constant value:
$$K_C = \frac{( 1.00 \times 10^{-2} )^{ 2 }}{( 1.40 \times 10^{-4} )^{ 2 }( 1.25 \times 10^{-5} )} = 4.1 \times 10^{8}$$