A-Level AQA Chemistry Fundamentals of Acids & Bases: The ionic product of water, K

The ionic product of water, K_w = 2.93 × 10^{-15} mol² dm^{-6} at 10 °C - AQA - A-Level Chemistry - Question 3 - 2017 - Paper 1

Question 3

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The ionic product of water, K_w = 2.93 × 10^{-15} mol² dm^{-6} at 10 °C. 0.3.1 Which is the correct expression for K_w? Tick (✓) one box. A K_w = [H_2O] B K_w ... show full transcript

Worked Solution & Example Answer:The ionic product of water, K_w = 2.93 × 10^{-15} mol² dm^{-6} at 10 °C - AQA - A-Level Chemistry - Question 3 - 2017 - Paper 1

Step 1

Which is the correct expression for K_w?

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Answer

The correct expression for the ionic product of water, $K_w$ , is given by Option C:

$K_w = [H^+][OH^-]$

Step 2

Calculate the pH of pure water at 10 °C.

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Answer

To calculate the pH of pure water at 10 °C, we know that in pure water:

$[H^+] = [OH^-]$

Using the expression for the ionic product of water:

$K_w = [H^+][OH^-] = 2.93 × 10^{-15}$

Letting $[H^+] = x$ , we have:

$K_w = x^2$

Thus,

$x = ext{√}(2.93 × 10^{-15}) = 1.71 × 10^{-8}$

Next, we calculate the pH:

= 7.77 $$ The pH of pure water at 10 °C is approximately 7.77.

Step 3

Suggest why this pure water at 10 °C is not alkaline.

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Answer

Pure water at 10 °C is not alkaline because the pH is 7.77, which is below 7. This indicates that pure water is neutral rather than alkaline. Alkaline solutions have a pH greater than 7; therefore, the presence of equal concentrations of $[H^+]$ and $[OH^-]$ maintains a neutral condition.

Step 4

Calculate the pH of a 0.0131 mol dm⁻³ solution of calcium hydroxide at 10 °C.

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Answer

Calcium hydroxide, $Ca(OH)_2$ , dissociates in water as follows:

ightarrow Ca^{2+} + 2OH^- $$ This means that for every mole of calcium hydroxide, two moles of hydroxide ions are produced. Therefore: $$ [OH^-] = 2 × 0.0131 = 0.0262 \, mol \, dm^{-3} $$ Now to find the pOH: $$ pOH = - ext{log}[OH^-] = - ext{log}(0.0262) \\ ≈ 1.58 $$ Using the relationship between pH and pOH: $$ pH + pOH = 14 $$ Thus: $$ pH = 14 - 1.58 \\ ≈ 12.42 $$ The pH of the 0.0131 mol dm⁻³ calcium hydroxide solution at 10 °C is approximately 12.42.

Step 5

Predict whether the pH of the magnesium hydroxide solution formed at 10 °C is larger than, smaller than or the same as the pH of the calcium hydroxide solution at 10 °C.

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Answer

The pH of the magnesium hydroxide solution is expected to be smaller than that of the calcium hydroxide solution. This is due to magnesium hydroxide being less soluble in water than calcium hydroxide, resulting in fewer hydroxide ions in solution. Therefore, the pH of the magnesium hydroxide solution will be lower than the pH of the calcium hydroxide solution, which is approximately 12.42.

The ionic product of water, K_w = 2.93 × 10^{-15} mol² dm^{-6} at 10 °C - AQA - A-Level Chemistry - Question 3 - 2017 - Paper 1

Worked Solution & Example Answer:The ionic product of water, K_w = 2.93 × 10^{-15} mol² dm^{-6} at 10 °C - AQA - A-Level Chemistry - Question 3 - 2017 - Paper 1

Which is the correct expression for K_w?

Calculate the pH of pure water at 10 °C.

Suggest why this pure water at 10 °C is not alkaline.

Calculate the pH of a 0.0131 mol dm⁻³ solution of calcium hydroxide at 10 °C.

Predict whether the pH of the magnesium hydroxide solution formed at 10 °C is larger than, smaller than or the same as the pH of the calcium hydroxide solution at 10 °C.

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