Instantaneous vs average rates; molar gas volumes: Practice Questions

What is the volume occupied by \( 0.250 \, \mathrm{mol} \) of oxygen gas at room temperature and pressure (r.t.p.)?

(Molar volume of gas at r.t.p. = \( 24.0 \, \mathrm{dm}^3 \, \mathrm{mol}^{-1} \))

A student reacts excess zinc granules with \( 100 \text{ cm}^3 \) of \( 0.40 \text{ mol dm}^{-3} \text{ HCl}(aq) \) at r.t.p. To monitor the rate, the mass of the flask and its contents was recorded. After 2 minutes, the mass had decreased by \( 0.104 \text{ g} \). Calculate the average rate of consumption of \( \text{H}^+(aq) \) ions during this 2-minute interval in \( \text{mol dm}^{-3} \text{ min}^{-1} \).
(Relative atomic mass: \( \text{H} = 1.0, \text{Cl} = 35.5, \text{Zn} = 65.4 \))

A graph of volume of hydrogen gas produced against time was plotted for the reaction between excess zinc and \( 50.0 \, \mathrm{cm}^3 \) of \( 1.0 \, \mathrm{mol} \, \mathrm{dm}^{-3} \, \mathrm{HCl} \). A tangent was drawn at \( t = 40 \, \mathrm{s} \). The tangent passes through the points \( (0 \, \mathrm{s}, 15 \, \mathrm{cm}^3) \) and \( (80 \, \mathrm{s}, 55 \, \mathrm{cm}^3) \). What is the instantaneous rate of consumption of \( \mathrm{H}^+(aq) \) ions at \( t = 40 \, \mathrm{s} \) in \( \mathrm{mol} \, \mathrm{s}^{-1} \)?

(Molar volume of gas at r.t.p. = \( 24.0 \, \mathrm{dm}^3 \, \mathrm{mol}^{-1} \))

What volume would \( 1.10 \, \mathrm{g} \) of nitrous oxide (\( \mathrm{N}_2\mathrm{O} \)) gas occupy at r.t.p.?

(Relative atomic masses: \( \mathrm{N} = 14.0, \mathrm{O} = 16.0 \); Molar volume of gas at r.t.p. = \( 24.0 \, \mathrm{dm}^3 \, \mathrm{mol}^{-1} \))

Consider the complete combustion of propane according to the following equation:
\( \mathrm{C}_3\mathrm{H}_8(g) + 5\mathrm{O}_2(g) \to 3\mathrm{CO}_2(g) + 4\mathrm{H}_2\mathrm{O}(l) \)
If \( 15.0 \, \mathrm{cm}^3 \) of propane is reacted with excess oxygen at room temperature and pressure, what is the volume of carbon dioxide produced?

Calculate the number of moles of gas present in a \( 6.0 \, \mathrm{dm}^3 \) sample of helium at room temperature and pressure (r.t.p.).
(Molar volume of gas at r.t.p. = \( 24.0 \, \mathrm{dm}^3 \, \mathrm{mol}^{-1} \))

A sample of \( 0.50\ g \) of a magnesium-aluminum alloy was reacted with excess hydrochloric acid. The total volume of hydrogen gas collected at r.t.p. was \( 540\ cm^3 \). Using the molar volume of \( 24.0\ dm^3\ mol^{-1} \), set up the algebraic equations required to determine the mass of magnesium in the alloy. (Relative atomic masses: \( Mg = 24.3 \), \( Al = 27.0 \))

A sample of magnesium carbonate reacts with excess dilute hydrochloric acid to produce carbon dioxide gas according to the equation:
\(\mathrm{MgCO}_3(s) + 2\mathrm{HCl}(aq) \to \mathrm{MgCl}_2(aq) + \mathrm{H}_2\mathrm{O}(l) + \mathrm{CO}_2(g)\)

(a) Calculate the number of moles of carbon dioxide gas produced from \(0.4215 \, \mathrm{g}\) of magnesium carbonate.

(b) Determine the volume of this carbon dioxide gas, in \(\mathrm{cm}^3\), measured at room temperature and pressure (r.t.p.).

(Relative atomic masses: \(\mathrm{C} = 12.0, \mathrm{O} = 16.0, \mathrm{Mg} = 24.3\); Molar volume of gas at r.t.p. = \(24.0 \, \mathrm{dm}^3 \, \mathrm{mol}^{-1}\))

In an experiment to study the rate of reaction between marble chips (\(\mathrm{CaCO}_3\)) and excess dilute hydrochloric acid, a student measured the volume of carbon dioxide gas collected over time:

Experimental Data:
Time (\(\mathrm{s}\)): \(0, 10, 20, 30, 40, 50, 60\)
Volume of \(\mathrm{CO}_2\) (\(\mathrm{cm}^3\)): \(0, 22, 38, 50, 58, 64, 68\)

(a) Calculate the average rate of reaction, in \(\mathrm{cm}^3 \, \mathrm{s}^{-1}\), during the first \(20\) seconds of the reaction.

(b) Calculate the average rate of reaction, in \(\mathrm{cm}^3 \, \mathrm{s}^{-1}\), between \(40\) and \(60\) seconds.

(c) Briefly describe how the student could determine the instantaneous rate of reaction at \(t = 30 \, \mathrm{s}\) from a graph of volume against time.