Answer
(a) $K_c = 0.082$
(b) $K_c = 0.29$
Work Step by Step
(a)
1. Write the equilibrium constant expression:
- The exponent of each concentration is equal to its balance coefficient.
$$K_C = \frac{[Products]}{[Reactants]} = \frac{[ NH_3 ] ^{ 2 }}{[ N_2 ][ H_2 ] ^{ 3 }}$$
2. Substitute the values and calculate the constant value:
$$K_C = \frac{( 0.25 )^{ 2 }}{( 0.11 )( 1.91 )^{ 3 }} = 0.082$$
(b)
1. Write the equilibrium constant expression:
- The exponent of each concentration is equal to its balance coefficient.
$$K_C = \frac{[Products]}{[Reactants]} = \frac{[ NH_3 ] }{[ N_2 ]^{1/2}[ H_2 ] ^{ 3/2 }}$$
2. Substitute the values and calculate the constant value:
$$K_C = \frac{( 0.25 )}{( 0.11 )^{1/2}( 1.91 )^{ 3/2 }} = 0.29$$
Alternative form:
Since the coefficients were divided by 2, the new kc is equal to the square root of the original one:
$$K_{c2} = \sqrt{K_{c1}} = \sqrt{0.082} = 0.29$$
