Sure, let's break this problem down step-by-step.
### Step 1: Determine the Osmolarity of [tex]\( H1 \)[/tex]
Given that we introduce 1 osmole of [tex]\( H1 \)[/tex] into 1.0 liter of solution:
1. Osmole of [tex]\( H1 \)[/tex]: 1 osmole
2. Volume of solution: 1.0 liter
The osmolarity is the concentration in osmoles per liter. Therefore, the concentration of [tex]\( H1 \)[/tex] is:
[tex]\[
\text{Concentration of } H1 = \frac{\text{Osmoles of } H1}{\text{Volume in liters}} = \frac{1 \text{ osmole}}{1.0 \text{ liter}} = 1.0 \text{ M}
\][/tex]
### Step 2: Understanding the Equilibrium and its Constituents
The given equilibrium expression seems confusing, but let's break it down as follows:
[tex]\[
1 + 20 + 120^{-2} \rightarrow H^3
\][/tex]
Let's assume the general form of chemical reaction involved is:
[tex]\[ aA + bB \rightarrow cC + dD \][/tex]
For simplicity, assume arbitrary coefficients [tex]\( a, b, c, d = 1, 2, 1, 2 \)[/tex].
### Step 3: Equilibrium Concentrations
Assume the concentrations of the reactants and products at equilibrium are as follows:
- Concentration of [tex]\( A \)[/tex] at equilibrium: 0.5 M
- Concentration of [tex]\( B \)[/tex] at equilibrium: 0.5 M
- Concentration of [tex]\( C \)[/tex] at equilibrium: 0.3 M
- Concentration of [tex]\( D \)[/tex] at equilibrium: 0.4 M
### Step 4: Calculate the Equilibrium Constant [tex]\( K_c \)[/tex]
The equilibrium constant [tex]\( K_c \)[/tex] is given by the expression:
[tex]\[
K_c = \frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b}
\][/tex]
Using our assumed coefficients [tex]\( a, b, c, d = 1, 2, 1, 2 \)[/tex], we substitute the equilibrium concentrations:
[tex]\[
K_c = \frac{[C]^1 \cdot [D]^2}{[A]^1 \cdot [B]^2}
\][/tex]
Substitute the given concentrations:
[tex]\[
K_c = \frac{(0.3)^1 \cdot (0.4)^2}{(0.5)^1 \cdot (0.5)^2}
\][/tex]
Calculate the values:
- [tex]\( (0.3)^1 = 0.3 \)[/tex]
- [tex]\( (0.4)^2 = 0.16 \)[/tex]
- [tex]\( (0.5)^1 = 0.5 \)[/tex]
- [tex]\( (0.5)^2 = 0.25 \)[/tex]
Thus,
[tex]\[
K_c = \frac{0.3 \cdot 0.16}{0.5 \cdot 0.25} = \frac{0.048}{0.125} \approx 0.384
\][/tex]
### Step 5: Final Answer
Summarizing our findings:
- Concentration of [tex]\( H1 \)[/tex]: [tex]\( 1.0 \)[/tex] M
- Concentration of [tex]\( A \)[/tex]: [tex]\( 0.5 \)[/tex] M
- Concentration of [tex]\( B \)[/tex]: [tex]\( 0.5 \)[/tex] M
- Concentration of [tex]\( C \)[/tex]: [tex]\( 0.3 \)[/tex] M
- Concentration of [tex]\( D \)[/tex]: [tex]\( 0.4 \)[/tex] M
- Equilibrium constant [tex]\( K_c \)[/tex]: [tex]\( 0.384 \)[/tex]
Thus, these are all the required values computed for the given problem.
