Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 13

At standard temperature and pressure, the molar volumes of \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) gases are 22.06 and \(22.40 \mathrm{~L}\), respectively. (a) Given the different molecular weights, dipole moments, and molecular shapes, why are their molar volumes nearly the same? (b) On cooling to $160 \mathrm{~K}$, both substances form crystalline solids. Do you expect the molar volumes to decrease or increase on cooling the gases to \(160 \mathrm{~K} ?\) (c) The densities of crystalline \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) at \(160 \mathrm{~K}\) are 2.02 and \(0.84 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. Calculate their molar volumes. (d) Are the molar volumes in the solid state as similar as they are in the gaseous state? Explain. (e) Would you expect the molar volumes in the liquid state to be closer to those in the solid or gaseous state?

Short Answer

Expert verified
The molar volumes of both Cl₂ and NH₃ gases are nearly the same at standard temperature and pressure because, according to the ideal gas law, all gases have the same molar volume under the same conditions. Upon cooling to 160 K, the molar volumes decrease as the kinetic energy of gas molecules decreases. In the solid state, Cl₂ and NH₃ have molar volumes of 35.10 cm³/mol and 20.27 cm³/mol, which are not as similar as in the gaseous state, as the differences in their molecular weights, dipole moments, and molecular shapes play a more significant role in the solid state. We expect that the molar volumes in the liquid state would be closer to those in the solid state due to stronger interactions between molecules in the liquid state compared to the gaseous state.

Step by step solution

01

a) The reason for nearly the same molar volumes

Both \(\mathrm{Cl}_{2}\) and \(\mathrm{NH}_{3}\) have nearly the same molar volumes despite their different molecular weights, dipole moments, and molecular shapes. The reason behind this similarity is because they are both gases at standard temperature and pressure, and according to the ideal gas law, all gases have the same molar volume under the same conditions. The ideal gas law is given by: \[PV=nRT\] Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. At standard temperature and pressure (STP), any gas will occupy a volume of 22.4 L per mole.
02

b) Molar volumes upon cooling to 160 K

Upon cooling the gases to 160 K, we expect that the molar volumes would decrease. The reason is that the kinetic energy of the gas molecules would decrease as we reduce the temperature, which makes the molecules move slower and occupy a relatively smaller volume.
03

c) Calculation of molar volumes in the solid state

We can calculate the molar volumes for crystalline Cl2 and NH3 at 160 K using the densities given: Density = \(\frac{Mass}{Volume}\) Molar Volume = \(\frac{Molar Mass}{Density}\) For Cl2: Molar mass of Cl2 = 2 x Molar mass of Cl = 2 x 35.45g/mol = 70.90 g/mol Molar volume of Cl2 = \(\frac{70.90 g/mol}{2.02 g/cm^3} = 35.10 cm^3/mol\) For NH3: Molar mass of NH3 = 14.01g/mol (N) + 3 x 1.008g/mol (H) = 17.030 g/mol Molar volume of NH3 = \(\frac{17.030 g/mol}{0.84 g/cm^3} = 20.27 cm^3/mol\)
04

d) Comparison of molar volumes in solid and gaseous states

The molar volumes of Cl2 and NH3 in the solid state are 35.10 cm^3/mol and 20.27 cm^3/mol, respectively, while in the gaseous state, they are 22.06 L/mol and 22.40 L/mol, respectively. We can see that the molar volumes in the solid state are not as similar as they are in the gaseous state. The differences in their molecular weights, dipole moments, and molecular shapes play a more significant role in the solid state than in the gaseous state, as the molecules are closer together in the solid state and interact more with each other.
05

e) Molar volumes in the liquid state

We expect that the molar volumes in the liquid state would be closer to those in the solid state than in the gaseous state. This is because the molecules are closer together in the liquid state compared to the gaseous state and have stronger interactions, similar to the solid state. The difference in molecular weights, dipole moments, and molecular shapes would play a more significant role in determining the molar volumes in the liquid state.

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Rationalize the difference in boiling points in each pair: (a) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O}\left(-23^{\circ} \mathrm{C}\right)\( and \)\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH} \quad\left(78^{\circ} \mathrm{C}\right),$ (b) \(\mathrm{CO}_{2}\left(-78.5^{\circ} \mathrm{C}\right)\) and $\mathrm{CS}_{2}\left(46.2^{\circ} \mathrm{C}\right),(\mathbf{c}) \mathrm{CH}_{3} \mathrm{COCH}_{3}\left(50.5^{\circ} \mathrm{C}\right)$ and \(\mathrm{CH}_{3} \mathrm{COOH}\left(101^{\circ} \mathrm{C}\right)\)

As a metal such as lead melts, what happens to (a) the average kinetic energy of the atoms and (b) the average distance between the atoms?

Suppose you have two colorless molecular liquids A and B whose boiling points are \(78^{\circ} \mathrm{C}\) and \(112^{\circ} \mathrm{C}\) respectively and both are at atmospheric pressure. Which of the following statements is correct? For each statement that is not correct, modify the statement so that it is correct. (a) Both A and \(B\) are liquids with identical vapor pressure at room temperature of \(25^{\circ} \mathrm{C} .(\mathbf{b})\) Liquid A must consist of nonpo- (c) Both lar molecules with lower molecular weight than B. liquids A and \(B\) have higher total intermolecular forces than water. (d) Liquid \(\mathrm{A}\) is more volatile than liquid \(\mathrm{B}\) because it has a lower boiling point. (e) At \(112^{\circ} \mathrm{C}\) both liquids have a vapor pressure of $1 \mathrm{~atm}$.

(a) How does the average kinetic energy of molecules compare with the average energy of attraction between molecules in solids, liquids, and gases? (b) Why does increasing the temperature cause a solid substance to change in succession from a solid to a liquid to a gas? (c) What happens to a gas if you put it under extremely high pressure?

Appendix \(\mathrm{B}\) lists the vapor pressure of water at various external pressures. (a) Plot the data in Appendix B,vapor pressure versus temperature $\left({ }^{\circ} \mathrm{C}\right) .$ From your plot, estimate the vapor pressure of water at body temperature, \(37^{\circ} \mathrm{C}\). (b) Explain the significance of the data point at $101.3 \mathrm{kPa}, 100^{\circ} \mathrm{C} .(\mathbf{c}) \mathrm{A}\( city at an altitude of \)1525 \mathrm{~m}$ above sea level has a barometric pressure of \(84.3 \mathrm{kPa}\). To what temperature would you have to heat water to boil it in this city? (d) A city at an altitude of \(150 \mathrm{~m}\) below sea level would have a barometric pressure of \(103.14 \mathrm{kPa}\). To what temperature would you have to heat water to boil it in this city?
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

Kinetics

Read Explanation

Physical Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free