Questions: Question For the following equilibrium: 2 A + B ⇌ C + 2 D If equilibrium concentrations are [A]=1.2 M, [B]=0.75 M, and [C]=1.4 M, and Kc=1.9, what is the equilibrium concentration of D? - Your answer should include two significant figures. Provide your answer below: M

Question For the following equilibrium: 2 A + B ⇌ C + 2 D If equilibrium concentrations are [A]=1.2 M, [B]=0.75 M, and [C]=1.4 M, and Kc=1.9, what is the equilibrium concentration of D? - Your answer should include two significant figures. Provide your answer below: M
Transcript text: Question For the following equilibrium: \[ 2 \mathrm{~A}+\mathrm{B} \rightleftharpoons \mathrm{C}+2 \mathrm{D} \] If equilibrium concentrations are $[\mathrm{A}]=1.2 \mathrm{M}$, $[\mathrm{B}]=0.75 \mathrm{M}$, and $[\mathrm{C}]=1.4 \mathrm{M}$, and $K_{c}=1.9$, what is the equilibrium concentration of D ? - Your answer should include two significant figures. Provide your answer below: $\square$ M
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Solution

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Solution Steps

Step 1: Write the Expression for the Equilibrium Constant

The equilibrium constant expression for the given reaction is: \[ K_c = \frac{[\mathrm{C}][\mathrm{D}]^2}{[\mathrm{A}]^2[\mathrm{B}]} \]

Step 2: Substitute Known Values into the Expression

Given: \[ [\mathrm{A}] = 1.2 \, \text{M}, \quad [\mathrm{B}] = 0.75 \, \text{M}, \quad [\mathrm{C}] = 1.4 \, \text{M}, \quad K_c = 1.9 \]

Substitute these values into the equilibrium constant expression: \[ 1.9 = \frac{(1.4)[\mathrm{D}]^2}{(1.2)^2(0.75)} \]

Step 3: Solve for the Equilibrium Concentration of D

First, simplify the denominator: \[ (1.2)^2 = 1.44 \] \[ 1.44 \times 0.75 = 1.08 \]

Now, the equation becomes: \[ 1.9 = \frac{1.4[\mathrm{D}]^2}{1.08} \]

Multiply both sides by 1.08 to isolate \([\mathrm{D}]^2\): \[ 1.9 \times 1.08 = 1.4[\mathrm{D}]^2 \] \[ 2.052 = 1.4[\mathrm{D}]^2 \]

Divide both sides by 1.4: \[ [\mathrm{D}]^2 = \frac{2.052}{1.4} \] \[ [\mathrm{D}]^2 = 1.4657 \]

Take the square root of both sides to find \([\mathrm{D}]\): \[ [\mathrm{D}] = \sqrt{1.4657} \approx 1.2107 \]

Step 4: Round to Two Significant Figures

Round the concentration of D to two significant figures: \[ [\mathrm{D}] \approx 1.2 \, \text{M} \]

Final Answer

\[ \boxed{1.2 \, \text{M}} \]

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