Answer:
1. [H₃O⁺] = 2.0 x 10⁻⁹ M.
[OH⁻] = 3.55 x 10⁻⁶ M.
The solution is basic.
2. [H₃O⁺] = 3.16 x 10⁻⁴ M.
[OH⁻] = 3.16 x 10⁻¹¹ M.
The solution is acidic.
3. [OH⁻] = 2.72 x 10⁻⁷ M.
pH = 7.435.
The solution is basic.
4. [OH⁻] = 9.89 x 10⁻³ M.
pH = 2.0.
The solution is acidic.
5. [H₃O⁺] = 1.82 x 10⁻⁵ M.
pH = 4.74.
The solution is acidic.
6.
[H₃O⁺] = 1.176 x 10⁻¹³ M.
pH = 12.93.
The solution is basic.
7. The solution is basic.
8. The solution is acidic.
9. The solution is acidic.
10. The solution is neutral.
Explanation:
pH = - log[H⁺],
pOH = - log[OH⁻],
Kw = [H⁺][OH⁻] = 10⁻¹⁴.
pH scale is a scale from 0 to 14, from which we can determine the nature of the solution:
1. Given pH = 8.55, Find: [H₃O⁺] and [OH⁻], Is this acidic, basic or neutral?
∵ pH = - log[H₃O⁺]
∴ 8.55 = - log[H₃O⁺]
∴ [H₃O⁺] = 2.0 x 10⁻⁹ M.
∵ Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [OH⁻] = 10⁻¹⁴/[H₃O⁺] = 10⁻¹⁴/(2.0 x 10⁻⁹ M) = 3.55 x 10⁻⁶ M.
∵ pH = 8.55 > 7,
∴ The solution is basic.
2. Given pH = 3.50, Find: [H₃O⁺] and [OH⁻], Is this acidic, basic or neutral?
∵ pH = - log[H₃O⁺]
∴ 3.50 = - log[H₃O⁺]
∴ [H₃O⁺] = 3.16 x 10⁻⁴ M.
∵ Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [OH⁻] = 10⁻¹⁴/[H₃O⁺] = 10⁻¹⁴/(3.16 x 10⁻¹⁴ M) = 3.16 x 10⁻¹¹ M.
∵ pH = 3.50 < 7,
∴ The solution is acidic.
3. Given [H₃O⁺] = 3.67 x 10⁻⁸ M, Find: [OH⁻] and pH, Is this acidic, basic or neutral?
∵ Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [OH⁻] = 10⁻¹⁴/[H₃O⁺] = 10⁻¹⁴/(3.67 x 10⁻⁸ M) = 2.72 x 10⁻⁷ M.
∵ pH = - log[H₃O⁺]
∴ pH = - log(3.67 x 10⁻⁸ M) = 7.435.
∵ pH = 7.435 > 7,
∴ The solution is basic.
4. Given [H₃O⁺] = 9.89 x 10⁻³ M, Find: [OH⁻] and pH, Is this acidic, basic or neutral?
∵ Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [OH⁻] = 10⁻¹⁴/[H₃O⁺] = 10⁻¹⁴/(9.89 x 10⁻³ M) = 9.89 x 10⁻³ M.
∵ pH = - log[H₃O⁺]
∴ pH = - log(9.89 x 10⁻³ M) = 2.0.
∵ pH = 2.0 < 7,
∴ The solution is acidic.
5. Given [OH⁻] = 5.5 x 10⁻¹⁰ M, Find: [H₃O⁺] and pH, Is this acidic, basic or neutral?
∵ Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [H₃O⁺] = 10⁻¹⁴/[OH⁻] = 10⁻¹⁴/(5.5 x 10⁻¹⁰ M) = 1.82 x 10⁻⁵ M.
∵ pH = - log[H₃O⁺]
∴ pH = - log(1.82 x 10⁻⁵ M) = 4.74.
∵ pH = 4.74 < 7,
∴ The solution is acidic.
6. Given [OH⁻] = 8.5 x 10⁻² M, Find: [H₃O⁺] and pH, Is this acidic, basic or neutral?
∵ Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [H₃O⁺] = 10⁻¹⁴/[OH⁻] = 10⁻¹⁴/(8.5 x 10⁻² M) = 1.176 x 10⁻¹³ M.
∵ pH = - log[H₃O⁺]
∴ pH = - log(1.176 x 10⁻¹³ M) = 12.93.
∵ pH = 12.93 > 7,
∴ The solution is basic.
7. Given [OH⁻] = 3.75 x 10⁻⁵ M, Is this acidic, basic or neutral? How do you know?
∵ Kw = [H₃O⁺][OH⁻] = 10⁻¹⁴.
∴ [H₃O⁺] = 10⁻¹⁴/[OH⁻] = 10⁻¹⁴/(3.75 x 10⁻⁵ M) = 2.67 x 10⁻¹⁰ M.
∵ pH = - log[H₃O⁺]
∴ pH = - log(2.67 x 10⁻¹⁰ M) = 9.57.
∵ pH = 9.57 > 7,
∴ The solution is basic.
8. Given [H₃O⁺] = 3.75 x 10⁻³ M, Is this acidic, basic or neutral? How do you know?
∵ pH = - log[H₃O⁺]
∴ pH = - log(3.75 x 10⁻³ M) = 2.43.
∵ pH = 2.43 < 7,
∴ The solution is acidic.
9. Given pH = 6.75, Is this acidic, basic or neutral? How do you know?
∵ pH = 6.75 < 7,
∴ The solution is acidic.
10. Given [H₃O⁺] = 1.00 x 10⁻⁷ M, Is this acidic, basic or neutral? How do you know?
∵ pH = - log[H₃O⁺]
∴ pH = - log(1.0 x 10⁻⁷ M) = 7.0.
∵ pH = 7.0,
∴ The solution is neutral.
