At sea level, water boils at 100 degrees c, while methane boils at -161 degrees c. which of these substances has a stronger force of attraction between its particles?

Because water has a higher boiling point, it has a stronger force of attraction between its particles. 
To get a substance to boil (transition to gas phase) the amount of kinetic energy between the particles has to exceed the attractive forces keeping the molecules near each other. Since temperature is an indirect measurement of the kinetic energy in a system, we can determine that a higher boiling point means greater attractive forces must be overcome.

Water (a polar molecule) has a large amount of hydrogen bonding creating a strong attractive force, which keeps the molecules near each other. Methane does not have hydrogen bonding, as it is a nonpolar molecule.

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