Answer
The missing values are, respectively (top to bottom):
$K_c = 1.45 \times 10^3$
$[H_2] = 0.249 \space M$
$[NH_3] = 4.39 \times 10^{-3} \space M$
Work Step by Step
1. Write the equilibrium constant expression:
- The exponent of each concentration is equal to its balance coefficient.
$$K_C = \frac{[Products]}{[Reactants]} = \frac{[ NH_3 ] ^{ 2 }}{[ N_2 ][ H_2 ] ^{ 3 }}$$
(a)
2. Substitute the values and calculate the constant value:
$$K_C = \frac{( 0.439 )^{ 2 }}{( 0.115 )( 0.105 )^{ 3 }} = 1.45 \times 10^{3}*$$
*The answer at the end of the book has a simple error, where there is a $10^{-3}$ , which does not make sense, as proven by these calculations.
(b)
3. Solve for the missing concentration:
$$ [H_2] = \sqrt[3]{\frac{[ NH_3 ]^{ 2 }}{[ N_2 ]\times K_c}}$$
4. Evaluate the expression:
$$ [H_2] = \sqrt[3]{\frac{( 0.128 )^{ 2 }}{( 0.110 )\times(9.6)}}$$
$$[H_2] = 0.249 \space M$$
(c)
5. Solve for the missing concentration:
$$ \sqrt[2]{K_c \times [ N_2 ][ H_2 ]^{ 3 }}{} = [NH_3]$$
6. Evaluate the expression:
$$ [NH_3] = \sqrt[2]{(0.0584) \times {( 0.120 )( 0.140 )^{ 3 }}{}}$$
$$[NH_3] = 4.39 \times 10^{-3} \space M$$
