For a look at pure logarithms, relate to Extremely important Experience 6 during the Point eleven

Note the newest Pattern

Erratic substances keeps reasonable boiling circumstances and you may apparently poor intermolecular relations; nonvolatile ingredients has higher boiling hot issues and you will apparently strong intermolecular connections.

Brand new rapid upsurge in vapor tension that have expanding heat during the Contour “The newest Vapor Demands of a lot H2o once the a purpose of Heat” allows us to fool around with natural logarithms to share this new nonlinear relationships given that a great linear you to definitely. nine “Crucial Knowledge 6”.

ln P = ? ? H vap Roentgen ( step 1 T ) + C Formula for a straight line : y = yards x + b

where ln P is the natural logarithm of the vapor pressure, ?H_vap is the enthalpy of vaporization, R is the universal gas constant [8.314 J/(mol·K)], T is the temperature in kelvins, and C is the y-intercept, which is a constant for any given line. A plot of ln P versus the inverse of the absolute temperature (1/T) is a straight line with a slope of ??H_vap/R. Equation 11.1, called the Clausius–Clapeyron equation A linear relationship that expresses the nonlinear relationship between the vapor pressure of a liquid and temperature: ln P = ? ? H vap / R T + C , where P is pressure, ? H vap is the heat of vaporization, R is the universal gas constant, T is the absolute temperature, and C is guardian soulmates bilgisayarda kullanımı a constant. The Clausius–Clapeyron equation can be used to calculate the heat of vaporization of a liquid from its measured vapor pressure at two or more temperatures. , can be used to calculate the ?H_vap of a liquid from its measured vapor pressure at two or more temperatures. The simplest way to determine ?H_vap is to measure the vapor pressure of a liquid at two temperatures and insert the values of P and T for these points into Equation 11.2, which is derived from the Clausius–Clapeyron equation:

ln ( P 2 P step one ) = ? ? H v an effective p R ( step 1 T dos ? 1 T step 1 )

Conversely, if we know ?H_vap and the vapor pressure P₁ at any temperature T₁, we can use Equation 11.2 to calculate the vapor pressure P₂ at any other temperature T₂, as shown in Example 6.

Example 6

From these data, calculate the enthalpy of vaporization (?H_vap) of mercury and predict the vapor pressure of the liquid at 160°C. (Safety note: mercury is highly toxic; when it is spilled, its vapor pressure generates hazardous levels of mercury vapor.)

A Use Equation 11.2 to obtain ?H_vap directly from two pairs of values in the table, making sure to convert all values to the appropriate units.

A The table gives the measured vapor pressures of liquid Hg for four temperatures. Although one way to proceed would be to plot the data using Equation 11.1 and find the value of ?H_vap from the slope of the line, an alternative approach is to use Equation 11.2 to obtain ?H_vap directly from two pairs of values listed in the table, assuming no errors in our measurement. We therefore select two sets of values from the table and convert the temperatures from degrees Celsius to kelvins because the equation requires absolute temperatures. Substituting the values measured at 80.0°C (T₁) and 120.0°C (T₂) into Equation 11.2 gives

ln ( 0.7457 torr 0.0888 torr ) = ? ? H vap 8.314 J/(mol · K) [ step one ( 120 + 273 ) K ? step 1 ( 80.0 + 273 ) K ] ln ( 8.398 ) = ? ? H vap 8.314 J · mol ? 1 · K ? step 1 ( ? 2.88 ? 10 ? cuatro K ? step 1 ) 2.thirteen = ? ? H vap ( ? 0.346 ? ten ? 4 ) J ? step 1 · mol ? H vap = 61,400 J/mol = 61 .cuatro kJ/mol