How to tell if a solution is acidic or basic from formula

Key Concepts

• A solution is defined as neutral if the concentration of hydrogen ions is the same as the concentration of hydroxide ions1:

  neutral solution: [H+] = [OH-]
  where [H+] = concentration of hydrogen ions in solution
  and [OH-] is the concentration of hydroxide ions in solution

• A solution is defined as acidic if the concentration of hydrogen ions is greater than the concentration of hydroxide ions:

  acidic solution: [H+] > [OH-]
  where [H+] = concentration of hydrogen ions in solution
  and [OH-] is the concentration of hydroxide ions in solution

• A solution is defined as basic2 if the concentration of hydrogen ions is less than the concentration of hydroxide ions:

  basic solution: [H+] < [OH-]
  where [H+] = concentration of hydrogen ions in solution
  and [OH-] is the concentration of hydroxide ions in solution

• Summary:

  acidic	neutral	basic
  [H+] > [OH-]	[H+] = [OH-]	[H+] < [OH-]

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Deciding if a Solution is Neutral

A solution is neutral if the concentration of hydrogen ions in solution is the same as the concentration of hydroxide ions in the solution.

neutral solution: [H+] = [OH-]

• If you know the concentration of hydrogen ions and hydroxide ions in a solution, then these must be the same in order for the solution to be neutral:

  example: an aqueous solution contains 0.15 mol L-1 H+(aq) and 0.15 mol L-1 OH-(aq)
  [H+(aq)] = [OH-(aq)] = 0.15 mol L-1 so solution is neutral

• If you know the concentration of the acid and the base in a neutralisation reaction, you will need to calculate the concentration of hydrogen ions and hydroxide ions in the resulting solution in order to decide if the resulting solution is neutral or not.

  example: 0.050 L of 0.02 mol L-1 hydrochloric acid is added to 0.025 L of 0.04 mol L-1 sodium hydroxide, will the resulting solution be neutral?

  	acid	base
  name formula	hydrochloric acid HCl(aq)	sodium hydroxide NaOH(aq)
  moles of each = concentration (mol L-1) × volume (L)	0.02 × 0.050 = 0.0010 mol	0.04 × 0.025 = 0.0010 mol
  strength	strong acid	strong base
  Dissociation Equation	HCl(aq) → H+(aq) + Cl-(aq)	NaOH(aq) → Na+(aq) + OH-(aq)
  moles H+ and OH-	moles H+ = moles HCl = 0.0010 mol	moles OH- = moles NaOH = 0.0010 mol
  assuming no reaction occurs: final solution concentrations = moles ÷ total volume (L)	[H+(aq)] = 0.0010 ÷ (0.050 + 0.025) = 0.013 mol L-1	[OH-(aq)] = 0.0010 ÷ (0.050 + 0.025) = 0.013 mol L-1
  Compare [H+(aq)] and [OH-(aq)] in final solution	[H+(aq)]	= [OH-(aq)]
  Decide if the final solution is neutral	Final solution is neutral because [H+(aq)] = [OH-(aq)]

• If you know the pH of an acid and the pH of a base in a neutralisation reaction, you will need to calculate the concentration of hydrogen ions and the concentration of hydroxide ions in each solution in order to determine if the final solution is neutral or not.

  example: At 25°C, 1 L of an aqueous acidic solution with a pH of 2.0 is added to 1 L of an aqueous basic solution with a pH of 12.0.
  Is the resulting solution neutral?

  	aqueous acidic solution	aqueous basic solution
  pH at 25oC	2.0	12.0
  calculate relevant concentrations for acidic solution and basic solution	[H+(aq)] = 10-pH = 10-2.0 = 0.010 mol L-1	[OH-(aq)] = 10(14-pH) = 10-(14-12) = 0.010 mol L-1
  calculate relevant moles for each solution moles = concentration × volume	moles (H+(aq)) = 0.010 × 1 = 0.010 mol	moles (OH-(aq)) = 0.010 × 1 = 0.010 mol
  assuming no reaction occurs: concentrations in final solution =moles ÷ total volume	[H+(aq)] = 0.010/(1 + 1) = 0.005 mol L-1	[OH-(aq)] = 0.010/(1 + 1) = 0.005 mol L-1
  Compare concentrations	[H+(aq)]	= [OH-(aq)]
  Decide if final solution will be neutral	Solution is neutral because [H+(aq)] = [OH-(aq)]

Deciding if a Solution is Acidic

A solution is acidic if the concentration of hydrogen ions in the solution is greater than the concentration of hydroxide ions in the solution.

acidic solution: [H+] > [OH-]

• If you know the concentration of hydrogen ions [H+] and the concentration of hydroxide ions [OH-] in the solution, then the solution is acidic if [H+] > [OH-]

  example: The concentration of hydrogen ions in a solution is 0.025 mol L-1 and the concentration of hydroxide ions in the same solution is 0.012 mol L-1. Is the solution acidic?
  [H+] = 0.025 mol L-1
  [OH-] = 0.012 mol L-1
  0.025 > 0.012 so [H+] > [OH-] and so the solution is acidic

• If you know the concentration of an aqueous acid and an aqueous base taking part in a neutralisation reaction, you will need to calculate the concentrations of H+(aq) and OH-(aq) in the final solution in order to decide if the final solution is acidic or not.

  example: 0.100 L of 0.02 mol L-1 hydrochloric acid is added to 0.025 L of 0.04 mol L-1 sodium hydroxide, will the resulting solution be acidic?

  	acid	base
  name formula	hydrochloric acid HCl(aq)	sodium hydroxide NaOH(aq)
  moles of each = concentration (mol/L) × volume (L)	0.20 × 0.100 = 0.020 mol	0.04 × 0.025 = 0.0010 mol
  strength	strong acid	strong base
  Dissociation Equation	HCl(aq) → H+(aq) + Cl-(aq)	NaOH(aq) → Na+(aq) + OH-(aq)
  moles H+ and OH-	moles H+ = moles HCl = 0.020 mol	moles OH- = moles NaOH = 0.0010 mol
  assuming no reaction occurs: final solution concentrations = moles ÷ total volume (L)	[H+(aq)] = 0.020 ÷ (0.100 + 0.025) = 0.016 mol L-1	[OH-(aq)] = 0.0010 ÷ (0.100 + 0.025) = 0.008 mol L-1
  Compare [H+(aq)] and [OH-(aq)] in final solution	[H+(aq)]	> [OH-(aq)]
  Decide if the final solution is acidic	Final solution is acidic because [H+(aq)] > [OH-(aq)]

• If you know the pH of an acid and the pH of a base in a neutralisation reaction, you will need to calculate the concentration of hydrogen ions and the concentration of hydroxide ions in each solution in order to determine if the final solution is acidic or not.

  example: At 25°C, 2 L of an aqueous acidic solution with a pH of 3.0 is added to 2 L of an aqueous basic solution with a pH of 9.0. Is the resulting solution acidic?

  	aqueous acidic solution	aqueous basic solution
  pH at 25°C	3.0	9.0
  calculate relevant concentrations for acidic solution and basic solution	[H+(aq)] = 10-pH = 10-3.0 = 0.0010 mol L-1	[OH-(aq)] = 10(14-pH) = 10-(14-9) = 0.000010 mol L-1
  calculate relevant moles for each solution = concentration × volume (L)	mol(H+(aq)) = 0.0010 × 2 = 0.0020 mol	mol(OH-(aq)) = 0.000010 × 2 = 0.000020 mol
  assuming no reaction occurs: calculate final concentrations = moles ÷ total volume	[H+(aq)] = 0.0020/(2 + 2) = 0.0005 mol L-1	[OH-(aq)] = 0.000020/(2 + 2) = 0.000005 mol L-1
  Compare concentrations	[H+(aq)]	> [OH-(aq)]
  Decide if final solution will be acidic	Solution is acidic because [H+(aq)] > [OH-(aq)]

Deciding if a Solution is Basic

A solution is basic if the concentration of hydrogen ions in the solution is less than the concentration of hydroxide ions in the solution:

basic solution: [H+] < [OH-]

• If you know the concentration of hydrogen ions [H+] and the concentration of hydroxide ions [OH-] in the solution, then the solution is basic if [H+] < [OH-]

  example: The concentration of hydrogen ions in a solution is 0.025 mol L-1 and the concentration of hydroxide ions in the same solution is 0.070 mol L-1. Is the solution basic?
  [H+] = 0.025 mol L-1
  [OH-] = 0.070 mol L-1
  0.025 < 0.070 so [H+] < [OH-] and so the solution is basic

• If you know the concentration of an aqueous acid and an aqueous base taking part in a neutralisation reaction, you will need to calculate the theoretical concentrations of H+(aq) and OH-(aq) in the final solution in order to decide if the final solution is basic or not.

  example: 0.100 L of 0.02 mol L-1 hydrochloric acid is added to 0.250 L of 0.09 mol L-1 sodium hydroxide, will the resulting solution be basic?

  	acid	base
  name formula	hydrochloric acid HCl(aq)	sodium hydroxide NaOH(aq)
  moles of each = concentration (mol/L) × volume (L)	0.20 × 0.100 = 0.020 mol	0.09 × 0.250 = 0.0225 mol
  strength	strong acid	strong base
  Dissociation Equation	HCl(aq) → H+(aq) + Cl-(aq)	NaOH(aq) → Na+(aq) + OH-(aq)
  moles H+ and OH-	moles H+ = moles HCl = 0.020 mol	moles OH- = moles NaOH = 0.0225 mol
  assuming no reaction occurs: concentrations in final solution = moles ÷ total volume (L)	[H+(aq)] = 0.020 ÷ (0.100 + 0.250) = 0.057 mol L-1	[OH-(aq)] = 0.0225 ÷ (0.100 + 0.250) = 0.064 mol L-1
  Compare [H+(aq)] and [OH-(aq)] in final solution	[H+(aq)]	< [OH-(aq)]
  Decide if the final solution is basic	Final solution is basic because [H+(aq)] < [OH-(aq)]

• If you know the pH of an acid and the pH of a base in a neutralisation reaction, you will need to calculate the concentration of hydrogen ions and the concentration of hydroxide ions in each solution in order to determine if the final solution is basic or not.

  example: At 25°C, 500 mL of an aqueous acidic solution with a pH of 3.0 is added to 500 mL of an aqueous basic solution with a pH of 13.0. Is the resulting solution basic?

  	aqueous acidic solution	aqueous basic solution
  pH at 25°C	3.0	13.0
  calculate relevant concentrations for each solution	[H+(aq)] = 10-pH = 10-3.0 = 0.0010 mol L-1	[OH-(aq)] = 10(14-pH) = 10-(14-13) = 0.10 mol L-1
  calculate relevant moles = concentration × volume (L)	moles(H+(aq)) = 0.0010 × 0.5 = 0.0005 mol	moles(OH-(aq)) = 0.10 × 0.5 = 0.05 mol
  assuming no reaction occurs: concentrations in final solution = moles ÷ total volume	[H+(aq)] = 0.0005/(0.5+0.5) = 0.0005 mol L-1	[OH-(aq)] = 0.05/(0.5+0 .5) = 0.05 mol L-1
  Compare concentrations	[H+(aq)]	< [OH-(aq)]
  Decide if final solution will be basic	Solution is basic because [H+(aq)] < [OH-(aq)]

Examples with Worked Solutions

Question 1. A solution is known contain 1.23 × 10-3 mol L-1 hydrogen ions and 1.23 × 10-4 mol L-1 hydroxide ions.
Is the solution acidic, basic or neutral?

1. Extract the data from the question:

   [H+] = 1.23 × 10-3 mol L-1
   [OH-] = 1.23 × 10-4 mol L-1

2. Compare [H+] and [OH-]

   [H+] > [OH-]

3. Decide if the solution is acidic, basic or neutral:

   Solution is acidic because [H+] > [OH-]

Question 2. At 25°C, 10 mL of aqueous sodium hydroxide solution is added to 100 mL of aqueous ethanoic (acetic) acid solution.
The pH of the resulting solution is 3.4.
Is the solution acidic, basic or neutral?

1. Extract the data from the question:

   volume of NaOH(aq) = 10 mL (not relevant to the question)
   volume of CH3COOH(aq) = 100 mL (not relevant to the question)
   pH of the final solution = 3.4 at 25°C

2. Calculate the concentration of hydrogen ions in the final solution:

   [H+] = 10-pH = 10-3.4 = 3.98 × 10-4 mol L-1

3. Calculate the concentration of hydroxide ions in the final solution:

   At 25°C Kw = [H+][OH-] = 1.0 × 10-14
   [OH-] = 1.0 × 10-4 ÷ [H+] = 1.0 × 10-14 ÷ 3.98 × 10-4 = 2.51 × 10-11 mol L-1

4. Compare [H+] and [OH-] in the final solution:

   [H+] = 3.98 × 10-4 mol L-1
   [OH-] = 2.51 × 10-11 mol L-1
   [H+] > [OH-]

5. Decide if the solution is acidic, basic or neutral:

   The solution is acidic because [H+] > [OH-]

Question 3. 0.15 g of solid sodium hydroxide is added to 0.025 L of 0.020 mol L-1 HCl(aq).
Is the resulting solution acidic, basic or neutral?

1. Extract the data from the question:

   mass NaOH = 0.15 g
   volume of HCl(aq) = V(HCl) = 0.025 L
   concentration of HCl(aq) = c(HCl(aq)) = 0.020 mol L-1

2. Calculate the concentration of hydrogen ions in the solution:

   hydrochloric acid is a strong acid so it fully dissociates in water: HCl → H+(aq) + Cl-(aq)
   [H+(aq)] = [HCl] = 0.020 mol L-1

3. Calculate moles of NaOH:

   moles = mass ÷ molar mass
   moles(NaOH) = 0.15 g ÷ (22.99 + 16.00 + 1.00) g/mol = 0.15 ÷ 39.99 = 3.75 × 10-3 mol

4. Calculate theoretical concentration of NaOH when the NaOH is added to the acid, assuming no reaction occurs :

   [NaOH(aq)] = moles ÷ volume (L) = 3.75 × 10-3 mol ÷ 0.025 L = 0.15 mol L-1

5. Calculate the concentration of OH- due to NaOH once NaOH is added to the acid:

   NaOH is a strong base so it fully dissociates in water: NaOH → Na+(aq) + OH-(aq)
   [OH-(aq)] = [NaOH] = 0.15 mol L-1

6. Compare [H+(aq)] and [OH-(aq)] in the solution:

   [H+(aq)] = 0.020 mol L-1
   [OH-(aq)] = 0.15 mol L-1
   [H+(aq)] < [OH-(aq)]

7. Decide if the solution is acidic, basic or neutral:

   The solution is basic because [H+(aq)] < [OH-(aq)]

Question 4. 28.0 mL of 0.012 mol L-1 HCl(aq) is added to 22.0 mL of 0.015 mol L-1 NaOH(aq).
Is the resulting solution acidic, basic or neutral?

1. Extract the data from the question:

   volume of HCl(aq) = 28.0 mL = 28.0/1000 = 0.0280 L
   concentration of HCl(aq) = 0.012 mol L-1
   volume of NaOH(aq) = 22.0 mL = 22.0/1000 = 0.0220 L
   concentration of NaOH(aq) = 0.015 mol L-1

2. Calculate the theoretical concentration of hydrogen ions in the final solution resulting from the hydrochloric acid, assuming no reaction occurs:

   moles HCl = concentration (mol/L) × volume (L) = 0.012 mol/L × 0.0280 L = 3.36 × 10-4 mol
   Hydrochloric acid is a strong acid so it fully dissociates in water: HCl → H+(aq) + Cl-(aq)
   moles of H+(aq) = moles HCl = 3.36 × 10-4 mol
   theoretical [H+(aq)] in the final solution = moles H+(aq) ÷ total volume of the solution in litres
   = 3.36 × 10-4 mol ÷ (0.028 L + 0.022 L) = 6.72 × 10-3 mol L-1

3. Calculate the theoretical concentration of hydroxide ions in the final solution resulting from the sodium hydroxide, assuming no reaction occurs:

   moles NaOH = concentration (mol/L) × volume (L) = 0.015 mol/L × 0.0220 L = 3.30 × 10-4 mol
   Sodium hydroxide is a strong base so it fully dissociates in water: NaOH → Na+(aq) + OH-(aq)
   moles of OH-(aq) = moles NaOH = 3.30 × 10-4 mol
   theoretical [OH-(aq)] in the final solution = moles OH-(aq) ÷ total volume of the solution in litres
   = 3.30 × 10-4 mol ÷ (0.028 L + 0.022 L) = 6.60 × 10-3 mol L-1

4. Compare [H+(aq)] and [OH-(aq)]

   [H+(aq)] = 6.72 × 10-3 mol L-1
   [OH-(aq)] = 6.60 × 10-3 mol L-1
   [H+(aq)] > [OH-(aq)]

5. Decide if the solution is acidic, basic or neutral:

   Final solution is acidic because [H+(aq)] > [OH-(aq)]

1. Since we are using the Arrhenius definition of acids, bases and neutralisation, it is quite acceptable to use H+ (or H+(aq)) to represent the hydrogen ion.

2. If the solution is aqueous, then we can use the terms alkali instead of base and alkaline instead of basic.