Question

The partial pressure of a perfect gas falls from 1 atm to 0.5 atm as it is consumed in a reaction at 298K. What is the change of chemical potential of the substance?

a) Positive

b) Negative

c) Zero

Answer 1

The change in chemical potential of a perfect gas as the partial pressure decreases from
`1 atm` to
`0.5 atm` at
`298K` is negative, indicating a decrease in chemical potential.

Step-by-step explanation:

When the partial pressure of a perfect gas falls from
`1 atm` to
`0.5 atm` as it is consumed in a reaction at
`298K` the chemical potential changes. According to the relationship
`Δμ = RT ln(P2/P1)`, where
`Δμ` is the change in chemical potential,
`R` is the universal gas constant
`T` is the temperature in Kelvin
`P2` is the final pressure and
`P1` is the initial pressure, we can determine the change.

Plugging in the values, we get
`Δμ = (8.314 J/mol·K)(298 K)`

ln
`(0.5 atm / 1 atm).`

The lne per mole of oll at temperature iollows:
`Δμ = -RT ln(2)` which yields a negative value indicating that the chemical potential of the gas decreases as the pressure decreases.