The normal boiling point of a liquid is

A. the temperature at which all three phases are in equilibrium.
B. the only temperature at which there can be equilibrium between the liquid and gas states.
C. the temperature at which the vapor pressure equals 760 mmHg.
D. the temperature above which the substance cannot exist as a liquid regardless of the pressure.
E. the temperature at which the amounts of liquid and gas are equal

I think the answer you want is C; however, I must point out that if you boil a liquid when the pressure is less than 760 (say 750 torr), the liquid will boil when the vapor pressure of the liquid is 750 and not 760 torr. I think the word "normal" in the post makes the assumption that standard pressure of 760 torr prevails.

To find the correct answer, let's go through each option one by one:

A. The temperature at which all three phases are in equilibrium: This refers to the point where the substance exists simultaneously in solid, liquid, and gas phases. However, the normal boiling point specifically relates to the liquid and gas phases, so this option is not the answer.

B. The only temperature at which there can be equilibrium between the liquid and gas states: This option suggests that the normal boiling point is the temperature at which the liquid and gas states can coexist. This is partly true but not a complete definition of the normal boiling point.

C. The temperature at which the vapor pressure equals 760 mmHg: The normal boiling point is indeed the temperature at which the vapor pressure of a liquid equals the standard atmospheric pressure, which is generally taken to be 760 mmHg. This option is likely the correct answer.

D. The temperature above which the substance cannot exist as a liquid regardless of the pressure: This refers to the critical temperature, which is different from the normal boiling point. So this option is not the answer.

E. The temperature at which the amounts of liquid and gas are equal: This is known as the boiling temperature but not specifically the normal boiling point. Therefore, this option is not the answer.

Based on our analysis, option C, "the temperature at which the vapor pressure equals 760 mmHg," is the most accurate description of the normal boiling point.