To solve the problem of arranging the given solutions in increasing hydronium ion concentration, we will analyze each solution step by step.
### Step 1: Analyze Solution P (0.1 M HCl)
- HCl is a strong acid and dissociates completely in water.
- Therefore, the concentration of hydronium ions \([H_3O^+]\) will be equal to the concentration of HCl.
- \([H_3O^+] = 0.1 \, M\)
### Step 2: Analyze Solution Q (0.1 M H₂SO₄)
- H₂SO₄ is also a strong acid and dissociates completely in water.
- Each molecule of H₂SO₄ produces two hydronium ions upon dissociation.
- Therefore, the concentration of hydronium ions will be:
- \([H_3O^+] = 2 \times 0.1 \, M = 0.2 \, M\)
### Step 3: Analyze Solution R (0.001 M NH₄OH)
- NH₄OH is a weak base and partially dissociates in water.
- The dissociation can be represented as:
\[ NH₄OH \rightleftharpoons NH₄^+ + OH^- \]
- The concentration of hydroxide ions \([OH^-]\) will be approximately equal to the concentration of NH₄OH, which is \(0.001 \, M\).
- Using the ion product of water \(K_w = [H_3O^+][OH^-] = 1.0 \times 10^{-14}\):
\[ [H_3O^+] = \frac{K_w}{[OH^-]} = \frac{1.0 \times 10^{-14}}{0.001} = 1.0 \times 10^{-11} \, M \]
### Step 4: Analyze Solution S (0.001 M Ca(OH)₂)
- Ca(OH)₂ is a strong base and dissociates completely in water:
\[ Ca(OH)₂ \rightarrow Ca^{2+} + 2OH^- \]
- Therefore, the concentration of hydroxide ions will be:
\[ [OH^-] = 2 \times 0.001 \, M = 0.002 \, M \]
- Using the ion product of water:
\[ [H_3O^+] = \frac{K_w}{[OH^-]} = \frac{1.0 \times 10^{-14}}{0.002} = 5.0 \times 10^{-13} \, M \]
### Step 5: Compare Hydronium Ion Concentrations
Now we will summarize the hydronium ion concentrations for each solution:
- Solution P: \([H_3O^+] = 0.1 \, M\)
- Solution Q: \([H_3O^+] = 0.2 \, M\)
- Solution R: \([H_3O^+] = 1.0 \times 10^{-11} \, M\)
- Solution S: \([H_3O^+] = 5.0 \times 10^{-13} \, M\)
### Step 6: Arrange in Increasing Order
To arrange the solutions in increasing order of hydronium ion concentration:
1. Solution R: \(1.0 \times 10^{-11} \, M\)
2. Solution S: \(5.0 \times 10^{-13} \, M\)
3. Solution P: \(0.1 \, M\)
4. Solution Q: \(0.2 \, M\)
Thus, the correct order of solutions in increasing hydronium ion concentration is:
**R < S < P < Q**
