Q52E - Chemistry (OpenStax)

Question

Question: A reaction is represented by this equation: \({K_c} = 5 \times 1{0^{ - 4}}\) 

(a) Write the mathematical expression for the equilibrium constant.

Step-by-Step Solution

Answer

The value of equilibrium constant \({K_c} = \frac{{(X) \cdot Y{)^2}}}{{{{(W)}^2}}}\) 

Step 1: Define Equilibrium constant

The Definition of equilibrium constant: a number that expresses the relationship between the amounts of products and reactants present at equilibrium in a reversible chemical reaction at a given temperature

Step 2: The expression of equilibrium constant

The reaction

The value of concentration \({K_c}{\rm{\;is\;}}5 \cdot {10^{ - 4}}\) 

 Let us write the mathematical expression for the equilibrium constant\({K_c} = \frac{{(X) \cdot {{(Y)}^2}}}{{{{(W)}^2}}}\) 

Question: A reaction is represented by this equation: \({K_c} = 5 \times 1{0^{ - 4}}\) (b) Using concentrations of \( \le 1M\) make up two sets of concentrations that describe a mixture of W, X, and Y at equilibrium

The Value of mixture concentration =\(\begin{array}{*{20}{c}}{(X) = 0.002{\rm{M}}}\\{(Y) = 0.1{\rm{M}}}\\{(W) = 0.2{\rm{M}}}\end{array}\)

Step 1: Define Equilibrium constant

The Definition of equilibrium constant: a number that expresses the relationship between the amounts of products and reactants present at equilibrium in a reversible chemical reaction at a given temperature

Step 2: Set 1 concentration of mixture

Let us make up two sets of concentrations that describe a mixture of \({\rm{W}},{\rm{X,\;}}\)and \({\rm{Y}}\) at equilibrium (concentrations \( \le 1{\rm{M}})\) 

The X concentration would be \(\begin{array}{*{20}{c}}{{K_c} = \frac{{(X) \cdot {{(Y)}^2}}}{{{{(W)}^2}}}}\\{(X) = \frac{{{K_c} \cdot {{(W)}^2}}}{{{{(Y)}^2}}}}\\{ = \frac{{5 \cdot {{10}^{ - 4}} \cdot {{(0.2)}^2}}}{{{{(0.1)}^2}}}}\\{ = 0.002{\rm{M}}}\end{array}\) 

The X would be \(\begin{array}{*{20}{c}}{(X) = 0.002M}\\{(Y) = 0.1M}\\{(W) = 0.2M}\end{array}\) 

Step 3: Set 2 concentration of mixture

The Let the concentration of \(X\)be \(0.2\) and the concentration of \({\rm{\;Y be\;}}0.01\) In this case, concentration of W would be

\(\begin{array}{*{20}{c}}{{K_c} = \frac{{(X) \cdot {{(Y)}^2}}}{{{{(W)}^2}}}}\\{{{(W)}^2} = \frac{{(X) \cdot {{(Y)}^2}}}{{{K_c}}}}\\{ = \frac{{(0.2) \cdot {{(0.01)}^2}}}{{5 \cdot {{10}^{ - 4}}}}}\\{ = 0.04}\\{(W) = \sqrt {0.04} }\\{ = 0.2}\end{array}\)

Set would be \(\begin{array}{*{20}{c}}{(X) = 0.02M}\\{(Y) = 0.01M}\\{(W) = 0.2M}\end{array}\)