Water is a polar molecule. It has an clectric dipole strength of p 6x 10-30 C m. This is roughly cquivalent to a proton and an electron separated by a distance of d = 4 x 10-11 m (about the radius of a hydrogen atom). In this problem, we will use Coulomb's law to compare the force between two protons (H*), a proton and a water molecule, and two water molecules. Use the arrangement of the charges shown in the figure for your calculations. (a) (b) (c) r (a) First, consider interactions at "short" distances. A chemical bond has a length on the order of r 0.1 nm. • What is the force between two protons separated by a distance of r 0.1 nm? What is the force between a proton and a water molecule separated by a distance of r 0.1 nm? What is the force between two water molecules separated by a distance of r = 0.1 nm?

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1 Intermolecular Forces
Water is a polar molecule. It has an electric dipole strength of p = 6 x 10-30 C - m. This is roughly equivalent to a proton
and an electron separated by a distance of d = 4 x 10-11 m (about the radius of a hydrogen atom).
In this problem, we will use Coulomb's law to compare the force between two protons (H*), a proton and a water
molecule, and two water molecules. Use the arrangement of the charges shown in the figure for your calculations.
(a)
r
(b)
(c)
r
(a) First, consider interactions at "short" distances. A chemical bond has a length on the order of r = 0.1 nm.
• What is the force between two protons separated by a distance of r = 0.1 nm?
• What is the force between a proton and a water molecule separated by a distance of r = 0.1 nm?
What is the force between two water molecules separated by a distance of r = 0.1 nm?
(b) Now consider a "long" distance: a separation of R = 1.0 nm. (This is about the length of ten hydrogen atoms lined
up next to each other.)
• What is the force between two protons separated by a distance of R = 1.0 nm?
• What is the force between a proton and a water molecule separated by a distance of R = 1.0 nm?
What is the force between two water molecules separated by a distance of R = 1.0 nm?
(c) Critical Thinking: You now have six different numbers. Compare ratios of forces. What do they tell you? Which
interactions (charge-charge, charge-dipole, dipole-dipole) are strongest at "short" distances? At "long" distances?
Which interactions decrease the fastest with increasing separation?
(d) Critical Thinking: Hydrogen bonding occurs in polar molecules – molecules with a permanent dipole mo-
ment. Based on your calculations in (a) and (b), over what distance do you think hydrogen bonding is important?
Transcribed Image Text:1 Intermolecular Forces Water is a polar molecule. It has an electric dipole strength of p = 6 x 10-30 C - m. This is roughly equivalent to a proton and an electron separated by a distance of d = 4 x 10-11 m (about the radius of a hydrogen atom). In this problem, we will use Coulomb's law to compare the force between two protons (H*), a proton and a water molecule, and two water molecules. Use the arrangement of the charges shown in the figure for your calculations. (a) r (b) (c) r (a) First, consider interactions at "short" distances. A chemical bond has a length on the order of r = 0.1 nm. • What is the force between two protons separated by a distance of r = 0.1 nm? • What is the force between a proton and a water molecule separated by a distance of r = 0.1 nm? What is the force between two water molecules separated by a distance of r = 0.1 nm? (b) Now consider a "long" distance: a separation of R = 1.0 nm. (This is about the length of ten hydrogen atoms lined up next to each other.) • What is the force between two protons separated by a distance of R = 1.0 nm? • What is the force between a proton and a water molecule separated by a distance of R = 1.0 nm? What is the force between two water molecules separated by a distance of R = 1.0 nm? (c) Critical Thinking: You now have six different numbers. Compare ratios of forces. What do they tell you? Which interactions (charge-charge, charge-dipole, dipole-dipole) are strongest at "short" distances? At "long" distances? Which interactions decrease the fastest with increasing separation? (d) Critical Thinking: Hydrogen bonding occurs in polar molecules – molecules with a permanent dipole mo- ment. Based on your calculations in (a) and (b), over what distance do you think hydrogen bonding is important?
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