KAITLYN ROGERS - Equilibrium Calculations.docx.pdf - Worksheet #1 ... - Free Printable

Let’s solve this step by step.

We are given five different chemical reactions and their equilibrium constants (K_eq). We need to find which reaction has the largest K_eq value — because that means it favors products the most at equilibrium.

Let’s list them out clearly:

1. Reaction:
\[
\frac{[O_2]^2}{[A_3^+][H_2O]^4} \quad K_{eq} = \frac{(0.689)^2}{(0.05)(0.012)} = 12.5
\]

2. Reaction:
\[
[O_2]^2 \quad K_{eq} = (6.5)^2 = 12 \times 10^3
\]
Wait — let’s calculate that:
\(6.5^2 = 42.25\), but it says “= 12 × 10³” → that’s 12,000? That doesn’t match. Let me check again.

Actually, looking closely:
It says:
\( K_{eq} = (6.5)^2 = 12 \times 10^3 \) — that must be a typo or miswriting. Because \(6.5^2 = 42.25\), not 12,000. But maybe it’s meant to be \( (6.5 \times 10^1)^2 \)? No — let’s read carefully.

Wait — perhaps it’s written as:
“K_eq = (6.5)^2 = 12 × 10^3” — that can’t be right numerically. Maybe it’s supposed to be:
K_eq = (6.5 × 10^1)^2? Then 65^2 = 4225 ≈ 4.2 × 10^3 — still not 12×10^3.

Alternatively, maybe it’s K_eq = 6.5 × 10^3? But it says squared.

Hold on — let’s look at the original image text again (as transcribed):

Second box:
[O₂]²
K_eq = (6.5)² = 12 × 10³

That math is wrong. 6.5 squared is 42.25, not 12,000. So likely, it’s a mistake in transcription or writing. Perhaps it’s meant to be:

K_eq = (6.5 × 10¹)² = 65² = 4225 ≈ 4.2 × 10³ — still not 12×10³.

Or maybe it’s K_eq = 6.5 × 10³? But then why write (6.5)²?

Wait — another possibility: maybe it’s K_eq = (6.5 × 10^1.5) or something? No, too complicated.

Perhaps the “= 12 × 10³” is separate? Like, they’re saying K_eq equals 12 × 10³, and the (6.5)² is part of the expression? But that doesn’t make sense.

Let me re-read the user’s transcription:

> (o₂)²
> K_eq = (6.5)² = 12 × 10³

This is inconsistent. Since we have to go with what’s written, and assuming the final number given is correct (because sometimes problems give you the calculated K_eq even if intermediate steps seem off), we’ll take the stated K_eq values as given for comparison.

So let’s list all the K_eq values as provided in the problem:

1. First reaction: K_eq = 12.5

2. Second reaction: K_eq = 12 × 10³ = 12,000

3. Third reaction: K_eq = (10⁻⁵) × (10⁻¹²) / 10⁻¹⁶
Let’s compute that:
Numerator: 10⁻⁵ × 10⁻¹² = 10⁻¹⁷
Divide by 10⁻¹⁶: 10⁻¹⁷ / 10⁻¹⁶ = 10⁻¹ = 0.1

But wait — the problem says:
K_eq = (10⁻⁵) × (10⁻¹²) / 10⁻¹⁶ = ?
Actually, looking back:
It says:
\[
\frac{[H^+][OH^-]}{} \quad K_{eq} = (10^{-5}) \times (10^{-12}) / 10^{-16}
\]
Wait — no denominator shown? In the transcription it says:
“K_eq = (10⁻⁵) × (10⁻¹²) / 10⁻¹⁶”

So yes:
(10⁻⁵)(10⁻¹²) = 10⁻¹⁷
10⁻¹⁷ / 10⁻¹⁶ = 10⁻¹ = 0.1

But the problem writes: “= 10⁻¹” — so K_eq = 0.1

4. Fourth reaction:
\[
\frac{[C O_2]^2}{[C O][O_2]} \quad K_{eq} = \frac{(0.08)^2}{(0.07)(0.04)} = 1.5
\]
Let’s verify:
(0.08)^2 = 0.0064
(0.07)(0.04) = 0.0028
0.0064 / 0.0028 ≈ 2.2857 — but problem says 1.5? Hmm, discrepancy.

Wait — maybe concentrations are different? Or perhaps it’s approximate? But since the problem states K_eq = 1.5, we’ll use that.

5. Fifth reaction:
\[
\frac{[L^+][Cl^-]}{} \quad K_{eq} = \frac{(0.76)(0.02)}{(0.76)(0.02)} = 0.0004
\]
Wait — numerator and denominator are the same? Then it should be 1. But it says = 0.0004? That doesn’t make sense.

Looking again:
Transcription says:
“K_eq = (0.76)(0.02) / (0.76)(0.02) = 0.0004”

That’s impossible — identical numerator and denominator should equal 1.

Unless... maybe it’s a typo? Perhaps it’s supposed to be different numbers? For example, maybe denominator is larger?

Alternatively, perhaps it’s K_eq = [products]/[reactants] and they wrote the same by mistake.

But since the problem explicitly says “= 0.0004”, we have to go with that for comparison purposes.

Now, let’s compile all the K_eq values as stated in the problem (even if some calculations seem off — we trust the given final K_eq for each):

1. K_eq = 12.5

2. K_eq = 12 × 10³ = 12,000

3. K_eq = 0.1 (from 10⁻¹)

4. K_eq = 1.5

5. K_eq = 0.0004

Now, comparing these:

- 12,000 (second reaction) is much larger than 12.5, 1.5, 0.1, and 0.0004.

Therefore, the second reaction has the largest equilibrium constant.

Even though there was confusion about how (6.5)² became 12,000, since the problem states K_eq = 12 × 10³ for that reaction, we accept that as given.

Final Answer: The second reaction has the largest K_eq value.