Molar concentrations, titration and gas volumes：練習問題

What is the volume occupied by \( 4.4\text{ g} \) of carbon dioxide gas, \( \text{CO}_2 \), at room temperature and pressure (RTP)?

(\( A_r: \text{C} = 12; \text{O} = 16 \))
(Molar gas volume at RTP = \( 24\text{ dm}^3\text{/mol} \))

A \( 50.0\text{ cm}^3 \) sample of a potassium hydroxide solution contains \( 1.40\text{ g} \) of \( \text{KOH} \).

Calculate the concentration of this solution in \( \text{mol/dm}^3 \).

(\( A_r: \text{K} = 39; \text{O} = 16; \text{H} = 1 \))

A student carries out a titration to find the concentration of a sulfuric acid solution. They find that \( 25.0\text{ cm}^3 \) of \( 0.100\text{ mol/dm}^3 \) sodium hydroxide, \( \text{NaOH} \), is exactly neutralised by \( 20.0\text{ cm}^3 \) of the sulfuric acid, \( \text{H}_2\text{SO}_4 \).

The equation for the reaction is:
\( 2\text{NaOH(aq)} + \text{H}_2\text{SO}_4\text{(aq)} \rightarrow \text{Na}_2\text{SO}_4\text{(aq)} + 2\text{H}_2\text{O(l)} \)

What is the concentration of the sulfuric acid in \( \text{mol/dm}^3 \)?

Calculate the volume, in \( \text{dm}^3 \), of \( 0.50 \text{ mol/dm}^3 \) sodium hydroxide solution required to react exactly with \( 12.0 \text{ dm}^3 \) of carbon dioxide gas at room temperature and pressure. Assume the molar gas volume is \( 24 \text{ dm}^3 \) and the reaction is:
\( 2\text{NaOH(aq)} + \text{CO}_2\text{(g)} \rightarrow \text{Na}_2\text{CO}_3\text{(aq)} + \text{H}_2\text{O(l)} \)

When \( 2.4 \text{ g} \) of an unknown metal \( \text{M} \) reacts with excess hydrochloric acid, \( 2.4 \text{ dm}^3 \) of hydrogen gas is produced at room temperature and pressure. Determine the relative atomic mass (\( A_r \)) of metal \( \text{M} \) assuming the reaction is:
\( M(s) + 2HCl(aq) \rightarrow MCl_2(aq) + H_2(g) \)
(Molar gas volume = \( 24 \text{ dm}^3 \))

Calculate the volume, in \( \text{dm}^3 \), of nitrogen gas required to produce \( 18.0 \text{ dm}^3 \) of ammonia at room temperature and pressure. Assume the molar gas volume is \( 24 \text{ dm}^3 \) and the reaction is:
\( \text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightarrow 2\text{NH}_3\text{(g)} \)

A solution of sulfuric acid has a concentration of 0.150 mol/dm³.
(a) Calculate the mass of pure \( H_2SO_4 \) required to prepare 250 cm³ of this solution.
(b) In a titration, 25.0 cm³ of this acid is neutralized by 30.0 cm³ of sodium hydroxide solution. Calculate the concentration of the sodium hydroxide solution in mol/dm³.

Equation: \( H_2SO_4(aq) + 2NaOH(aq) \rightarrow Na_2SO_4(aq) + 2H_2O(l) \)
(Relative atomic masses: \( H = 1, S = 32, O = 16 \))

A student reacts calcium carbonate, \(\text{CaCO}_3\), with excess hydrochloric acid, \(\text{HCl}\), to produce carbon dioxide gas according to the equation:

\(\text{CaCO}_3(s) + 2\text{HCl}(aq) \rightarrow \text{CaCl}_2(aq) + \text{H}_2\text{O}(l) + \text{CO}_2(g)\)

a) Calculate the number of moles in \(5.0\text{ g}\) of calcium carbonate.
(Relative atomic masses: \(\text{Ca} = 40, \text{C} = 12, \text{O} = 16\))

b) Using your answer to part a, determine the volume of carbon dioxide gas produced at room temperature and pressure (RTP).
(Molar gas volume at RTP = \(24\text{ dm}^3/\text{mol}\))

c) If the carbon dioxide produced was instead dissolved to make a \(250\text{ cm}^3\) solution, what would be its molar concentration in \(\text{mol/dm}^3\)?