Consider the statements (a) to (e) below. Assume that \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) behave ideally. State whether each of the following statements is true or false. For each false statement, explain how you would change it to make it a true statement. (a) Under the same conditions of temperature and pressure, the average kinetic energy of \(\mathrm{O}_{2}\) molecules is less than that of \(\mathrm{H}_{2}\) molecules. (b) Under the same conditions of temperature and pressure, \(\mathrm{H}_{2}\) molecules move faster, on average, than \(\mathrm{O}_{2}\) molecules. (c) The volume of \(1.00 \mathrm{mol}\) of \(\mathrm{H}_{2}(\mathrm{g})\) at \(25.0^{\circ} \mathrm{C}\) 1.00 atm is \(22.4 \mathrm{L}\) (d) The volume of \(2.0 \mathrm{g} \mathrm{H}_{2}(\mathrm{g})\) is equal to the volume of \(32.0 \mathrm{g} \mathrm{O}_{2}(\mathrm{g}),\) at the same temperature and pressure. (e) In a mixture of \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) gases, with partial pressures \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}^{\prime}}\) respectively, the total pressure is the larger of \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}}\).

Step by step solution

01

Statement (a) Analysis

Under the same conditions of temperature and pressure, the average kinetic energy of gases is same, irrespective of their molecular mass. Therefore, the statement (a) is false. A correct statement would be, 'Under the same conditions of temperature and pressure, the average kinetic energy of \(O_2\) molecules is the same as that of \(H_2\) molecules.'

02

Statement (b) Analysis

As per the kinetic theory of gases, lighter gas molecules move faster than heavier gas molecules at the same temperature. Therefore, the statement \(H_2\) molecules move faster, on average, than \(O_2\) molecules under the same conditions of temperature and pressure, is true.

03

Statement (c) Analysis

As per Avogadro's law, 1 mol of an ideal gas indeed occupies a volume of \(22.4 L\) at standard temperature and pressure (0ºC and 1 atm). However, the statement mentions a temperature of \(25.0ºC\), which is not standard. Thus, the statement is false. A correct version would state, 'The volume of 1.00 mol of \(H_2(g)\) at \(0.0ºC\) and 1.00 atm is \(22.4 L\)'.

04

Statement (d) Analysis

According to Avogadro's principle, equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. Therefore, the volume of \(2.0 g H_2(g)\) (equivalent to 1 mol) is equal to the volume of \(32.0 g O_2(g)\) (also equivalent to 1 mol) at the same temperature and pressure, making this statement true.

05

Statement (e) Analysis

According to Dalton's law of partial pressures, the total pressure of a gas mixture is the sum of the partial pressures of the individual gases in the mixture. Thus, the statement is false. A correct statement would be: 'In a mixture of \(H_2\) and \(O_2\) gases, with partial pressures \(P_{H_{2}}\) and \(P_{O_{2}}\) respectively, the total pressure is \(P_{H_{2}} + P_{O_{2}} \)'.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!