Video Transcript
How much heat in kilojoules is
released when 0.13 moles of methanol gas at 64.7 degrees Celsius are converted to
methanol liquid? Take the standard enthalpy of
vaporization of methanol to be positive 35.2 kilojoules per mole. Give your answer to two decimal
places.
In this question, we are told that
a sample of methanol is converted from gas to liquid at a specific temperature. The name of the physical change
that occurs when the gaseous form of a substance is transformed to the liquid form
is condensation. We are told that during
condensation, energy in the form of heat is released. Our job in answering this question
is to determine how much heat is released when 0.13 moles of methanol gas
condenses. The provided symbol Δ𝐻 vap
represents the standard enthalpy of vaporization. The standard enthalpy of
vaporization is the enthalpy change when one mole of a substance transforms from a
liquid to a gas at standard temperature and pressure.
Vaporization, which is the
conversion from liquid to gas, is the opposite of condensation. Energy must be absorbed by the
liquid methanol in order for vaporization to happen. The given value of the standard
enthalpy of vaporization for methanol is positive 35.2 kilojoules per mole. This means that if we had one mole
of liquid methanol, it would need to absorb 35.2 kilojoules of energy to be fully
converted to a gas. Processes that require the
absorption of energy are endothermic, and their associated standard enthalpy values
are positive.
To solve this problem, we’ll need
to make use of the standard enthalpy of condensation, but we aren’t given this
value. We already know that condensation
is the opposite process of vaporization, so we can define the standard enthalpy of
condensation as the enthalpy change when one mole of substance transforms from a gas
to a liquid at standard conditions. The size of the standard enthalpy
of condensation will be the same as the standard enthalpy of vaporization. However, the sign will be the
opposite. Because heat is released during
condensation, it’s classified as an exothermic process. We will need to use a negative sign
when writing the value of the enthalpy of condensation. Let’s write negative 35.2
kilojoules per mole as the standard enthalpy of condensation for methanol.
If one mole of gaseous methanol
releases 35.2 kilojoules of energy at standard conditions, enough energy will have
been lost for all of the gas to be converted to a liquid. However, in this problem, the given
amount of moles of methanol is quite a bit less, 0.13 moles. We’d expect less energy to be
released during condensation. To determine the specific amount of
energy released when 0.13 moles of methanol gas condenses at standard conditions,
we’ll need to multiply our given amount of moles, 0.13, by the standard enthalpy for
condensation of methanol, negative 35.2 kilojoules per mole. This gives us an answer of negative
4.576 kilojoules.
Finally, we’ll need to round our
answer to two decimal places. Our final rounded answer is
negative 4.58 kilojoules, which is the amount of heat released when 0.13 moles of
methanol gas condenses at 64.7 degrees Celsius.
