A particular compound has an enthalpy of vaporization of 28900 J/mol. At 278 K it has a vapor pressure of 103 mmHg. What is its vapor pressure at 309 K? (R = 8.31 J/(K· mol))a. 29.4mmhgb. 99.5mmhgc. 107mmhgd. 194mmhge. 361mmhg

Respuesta :

Answer:

[tex]E\text{ : 361 mmHg}[/tex]

Explanation:

Here, we want to get the vapour pressure of the compound at the given temperature

We can use the Clausius-Clapeyron equation for this

Mathematically, we have this as:

[tex]\ln (\frac{P_1}{P_2})\text{ = -}\frac{\Delta H}{R}(\frac{1}{T_1}-\frac{1}{T_2})[/tex]

So,let us identify the values:

P1 = 103 mmHg

P2 = ?

ΔH = 28,900

R = 8.31

T1 = 278 K

T2 = 309 K

We now proceed to substitute these values into the equation above as follows:

[tex]\begin{gathered} \ln (\frac{103}{P_2})\text{ = -}\frac{28900}{8.31}(\frac{1}{278}-\frac{1}{309}) \\ \\ \ln (\frac{103}{P_2})\text{ = -3477.74 (}\frac{31}{85902}) \\ \\ \ln (\frac{103}{P_2})\text{ = -1.255} \\ \\ e^{-1.255}\text{ = }\frac{103}{P_2} \\ P_2\text{ = 361 mmHg} \end{gathered}[/tex]