# Having a peek at pure logarithms, refer to Extremely important Enjoy 6 for the Part step step 11

August 3, 2022

Having a peek at pure logarithms, refer to Extremely important Enjoy 6 for the Part step step 11
Notice the fresh new Development

Unpredictable compounds possess low boiling facts and you can relatively poor intermolecular affairs; nonvolatile ingredients have large boiling hot facts and you may relatively solid intermolecular affairs.

Brand new exponential increase in vapor pressure which have increasing heat during the Shape “The latest Steam Demands of a lot Drinking water given that a purpose of Heat” allows us to have fun with absolute logarithms to fairly share the nonlinear dating since the a great linear that. nine “Essential Experience six”.

ln P = ? ? H vap Roentgen ( step one T ) + C Formula to possess a straight-line : y = m x + b

where ln P is the natural logarithm of the vapor pressure, ?Hvap 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 ??Hvap/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 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 ?Hvap of a liquid from its measured vapor pressure at two or more temperatures. The simplest way to determine ?Hvap 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 dos P 1 ) = ? ? H v good p Roentgen ( step one T 2 ? step one T step 1 )

Conversely, if we know ?Hvap 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 (?Hvap) 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 ?Hvap 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 ?Hvap from the slope of the line, an alternative approach is to use Equation 11.2 to obtain ?Hvap 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) [ 1 ( 120 + 273 ) K https://datingranking.net/tr/huggle-inceleme/? step 1 ( 80.0 + 273 ) K ] ln ( 8.398 ) = ? ? H vap 8.314 J · mol ? 1 · K ? 1 ( ? dos.88 ? 10 ? 4 K ? step one ) dos.thirteen = ? ? H vap ( ? 0.346 ? 10 ? 4 ) J ? step one · mol ? H vap = 61,eight hundred J/mol = 61 .4 kJ/mol

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