Question

Solve for x and list step by step.Kc = 7

Answer 1

`x\text{ = }\frac{-1.45\text{ - 0.847i}}{12}\text{ or }\frac{-1.45\text{ + 0.847i}}{12}`

Explanation

The equation of a chemical equilibrium reaction is given below as

`Kc\text{ = }(0.04-0.4x+x^2)/(0.0225+0.15x+x^2)`

Recall that, Kc = 7

The next step is to substitute the value of Kc = 7 into the above equation

`7\text{ = }(0.04-0.4x+x^2)/(0.0225+0.15x+x^2)`

The next step is to cross multiply

The next step is to solve for x in the equation using the general quadratic formula

Recall that,

Relating the two equations together, then, we have the following

a = -6

b = -1.45

c = -0.1175

`\begin{gathered} x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ x\text{ = }\frac{-(-1.45)\text{ }\pm\sqrt[]{-1.45^2\text{ - (4 }\cdot-\text{ 6 }\cdot\text{ -0.1175)}}}{2\cdot\text{ -6}} \\ x\text{ = }\frac{1.45\text{ }\pm\sqrt[]{2.1025\text{ - }(2.82)}}{-12} \\ x\text{ = }\frac{\text{ 1.45 }\pm\sqrt[]{-0.7175}}{-12} \\ x\text{ = }\frac{1.45\pm\sqrt[]{0.7175}\text{ }\sqrt[]{-1}}{-12} \\ \text{ recall that, }\sqrt[]{-1\text{ }}\text{ = i} \\ x\text{ = }\frac{1.45\pm\sqrt[]{0.7175}\text{ i}}{-12} \\ x\text{ = }\frac{1.45\text{ }\pm0.847i}{-12} \\ x\text{ = }\frac{1.45\text{ + 0.847i}}{-12}\text{ or }\frac{1.45-\text{ 0.847i}}{-12} \\ x\text{ = }\frac{-1.45\text{ - 0.847i}}{12}\text{ or }\frac{-1.45\text{ + 0.847i}}{12} \end{gathered}`