Question

The vapor pressure of water is 1.00 atm at 373 K, and the enthalpy of vaporization is 40.68 kJ mol!. Estimate the vapor pressure at temperature 363 and 383 K respectively. Ansl = 0.697 atm, Ans2 = 1.41 atm

Answer 1

To estimate the vapor pressure at temperatures 363 K and 383 K, we can use the Clausius-Clapeyron equation.

Step-by-step explanation:

To estimate the vapor pressure of water at temperatures 363 K and 383 K, we can use the Clausius-Clapeyron equation:

ln(P₂/P₁) = -(ΔHvap/R) * (1/T₂ - 1/T₁)

Where P₁ is the vapor pressure at 373 K, P₂ is the vapor pressure at the desired temperatures, ΔHvap is the enthalpy of vaporization, R is the ideal gas constant, T₁ is 373 K, T₁ is the desired temperature in Kelvin.

For temperature 363 K:

ln(P₂/1) = -(40.68 kJ/mol / (8.314 J/molK)) * (1/363 - 1/373)

P₂ = 0.697 atm

For temperature 383 K:

ln(P₂/1) = -(40.68 kJ/mol / (8.314 J/molK)) * (1/383 - 1/373)

P₂ = 1.41 atm

Answer 2

The vapor pressure at temperature 363 K is 0.6970 atm

The vapor pressure at 383 K is 1.410 atm

Step-by-step explanation:

To calculate
`\Delta H_(vap)` of the reaction, we use clausius claypron equation, which is:

`\ln((P_2)/(P_1))=(\Delta H_(vap))/(R)[(1)/(T_1)-(1)/(T_2)]`

where,

`P_1` = vapor pressure at temperature
`T_1`

`P_2` = vapor pressure at temperature
`T_2`

`\Delta H_(vap)` = Enthalpy of vaporization

R = Gas constant = 8.314 J/mol K

1)
`\Delta H_(vap)=40.68 kJ/mol=40680 J/mol`

`T_1` = initial temperature =363 K

`T_2` = final temperature =373 K

`P_2=1 atm, P_1=?`

Putting values in above equation, we get:

`\ln((1 atm)/(P_1))=(40680 J/mol)/(8.314J/mol.K)[(1)/(363)-(1)/(373)]`

`P_1=0.69671 atm \approx 0.6970 atm`

The vapor pressure at temperature 363 K is 0.6970 atm

2)
`\Delta H_(vap)=40.68 kJ/mol=40680 J/mol`

`T_1` = initial temperature =373 K

`T_2` = final temperature =383 K

`P_1=1 atm, P_2?`

Putting values in above equation, we get:

`\ln((P_2)/(1 atm))=(40680 J/mol)/(8.314J/mol.K)[(1)/(373)-(1)/(383)]`

`P_2=1.4084 atm \approx 1.410 atm`

The vapor pressure at 383 K is 1.410 atm