Questions: Advanced General Chemistry Calculating an equilibrium constant from an equilibrium composition Ammonia decomposes to form nitrogen and hydrogen, like this: 2 NH3(g) → N2(g) + 3 H2(g) Also, a chemist finds that at a certain temperature the equilibrium mixture of ammonia, nitrogen, and hydrogen has the following composition: compound concentration at equilibrium NH3 0.53 M N2 0.11 M H2 0.94 M Calculate the value of the equilibrium constant Kc for this reaction. Round your answer to 2 significant digits. Kc =

Advanced General Chemistry
Calculating an equilibrium constant from an equilibrium composition

Ammonia decomposes to form nitrogen and hydrogen, like this:
2 NH3(g) → N2(g) + 3 H2(g)

Also, a chemist finds that at a certain temperature the equilibrium mixture of ammonia, nitrogen, and hydrogen has the following composition:
compound concentration at equilibrium
NH3 0.53 M
N2 0.11 M
H2 0.94 M

Calculate the value of the equilibrium constant Kc for this reaction. Round your answer to 2 significant digits.
Kc =

Transcript text: Advanced General Chemistry Calculating an equilibritum constant from an equillbritum composition Ammonia decomposes to form nitrogen and hydrogen, like this: \[ 2 \mathrm{NH}_{3}(g) \rightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \] Also, a chemist finds that at a certain temperature the equilibrium mixture of ammonia, nitrogen, and hydrogen has the following composition: \begin{tabular}{|c|c|} \hline compound & concentration at equilibrium \\ \hline $\mathrm{NH}_{3}$ & 0.53 M \\ \hline $\mathrm{N}_{2}$ & 0.11 M \\ \hline $\mathrm{H}_{2}$ & 0.94 M \\ \hline \end{tabular} Calculate the value of the equilibrium constant $K_{c}$ for this reaction. Round your answer to 2 significant digits. \[ K_{c}= \] $\square$ Enlanation Check

Solution

Solution Steps

Step 1: Write the Expression for the Equilibrium Constant

For the reaction: \[ 2 \mathrm{NH}_{3}(g) \rightarrow \mathrm{N}_{2}(g) + 3 \mathrm{H}_{2}(g) \]

The equilibrium constant expression $ K_c $ is given by: \[ K_c = \frac{[\mathrm{N}_2][\mathrm{H}_2]^3}{[\mathrm{NH}_3]^2} \]

Step 2: Substitute the Equilibrium Concentrations

Given the equilibrium concentrations: \[ [\mathrm{NH}_3] = 0.53 \, \text{M}, \quad [\mathrm{N}_2] = 0.11 \, \text{M}, \quad [\mathrm{H}_2] = 0.94 \, \text{M} \]

Substitute these values into the equilibrium constant expression: \[ K_c = \frac{(0.11) \times (0.94)^3}{(0.53)^2} \]

Step 3: Calculate the Equilibrium Constant

First, calculate the numerator: \[ (0.11) \times (0.94)^3 = 0.11 \times 0.8306 = 0.0914 \]

Next, calculate the denominator: \[ (0.53)^2 = 0.2809 \]

Now, divide the numerator by the denominator: \[ K_c = \frac{0.0914}{0.2809} \approx 0.3255 \]

Step 4: Round to Two Significant Digits

Round the calculated value to two significant digits: \[ K_c \approx 0.33 \]