Problem: The vapor pressure for pure water and pure acetone is measured as a function of temperature. In each case, a graph of the log of the vapor pressure versus 1/T is found to be a straight line. The slope of the line for water is -4895 K and the slope of the line for acetone is -3765 K. What is the ΔHvap of water?

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The vapor pressure of a liquid rises exponentially with the increase in temperature. This relation is simplified if ln(P) is plotted against 1/T and the graph becomes a straight line. The equation for such a plot is:


<math xmlns="http://www.w3.org/1998/Math/MathML"><menclose mathcolor="#0000FF" notation="box"><mi>l</mi><mi>n</mi><mfenced><mi>P</mi></mfenced><mo>&#xA0;</mo><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&#xA0;</mo><mo>&#x2206;</mo><msub><mi>H</mi><mrow><mi>v</mi><mi>a</mi><mi>p</mi></mrow></msub></mrow><mi>R</mi></mfrac><mfenced><mfrac><mn>1</mn><mi>T</mi></mfrac></mfenced><mo>+</mo><mi>C</mi><mo>&#xA0;</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mfenced><mn>1</mn></mfenced></menclose><mspace linebreak="newline"></mspace><mi>w</mi><mi>h</mi><mi>e</mi><mi>r</mi><mi>e</mi><mo>,</mo><mo>&#xA0;</mo><mi>P</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>P</mi><mi>r</mi><mi>e</mi><mi>s</mi><mi>s</mi><mi>u</mi><mi>r</mi><mi>e</mi><mspace linebreak="newline"></mspace><mo>&#x2206;</mo><msub><mi>H</mi><mrow><mi>v</mi><mi>a</mi><mi>p</mi></mrow></msub><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>e</mi><mi>n</mi><mi>t</mi><mi>h</mi><mi>a</mi><mi>l</mi><mi>p</mi><mi>y</mi><mo>&#xA0;</mo><mi>c</mi><mi>h</mi><mi>a</mi><mi>n</mi><mi>g</mi><mi>e</mi><mo>&#xA0;</mo><mi>o</mi><mi>f</mi><mo>&#xA0;</mo><mi>v</mi><mi>a</mi><mi>p</mi><mi>o</mi><mi>r</mi><mi>i</mi><mi>z</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mspace linebreak="newline"></mspace><mi>R</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>i</mi><mi>d</mi><mi>e</mi><mi>a</mi><mi>l</mi><mo>&#xA0;</mo><mi>g</mi><mi>a</mi><mi>s</mi><mo>&#xA0;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>t</mi><mspace linebreak="newline"></mspace><mi>T</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>t</mi><mi>e</mi><mi>m</mi><mi>p</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>e</mi><mspace linebreak="newline"></mspace><mi>C</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>y</mi><mo>-</mo><mi>i</mi><mi>n</mi><mi>t</mi><mi>e</mi><mi>r</mi><mi>c</mi><mi>e</mi><mi>p</mi><mi>t</mi><mo>&#xA0;</mo><mi>o</mi><mi>f</mi><mo>&#xA0;</mo><mi>t</mi><mi>h</mi><mi>e</mi><mo>&#xA0;</mo><mi>s</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>g</mi><mi>h</mi><mi>t</mi><mo>&#xA0;</mo><mi>l</mi><mi>i</mi><mi>n</mi><mi>e</mi></math>


Now, recall that the equation for a straight line is:


<math xmlns="http://www.w3.org/1998/Math/MathML"><menclose mathcolor="#0000FF" notation="box"><mi>y</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>C</mi><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mo>-</mo><mfenced><mn>2</mn></mfenced></menclose><mspace linebreak="newline"></mspace><mi>w</mi><mi>h</mi><mi>e</mi><mi>r</mi><mi>e</mi><mo>,</mo><mo>&#xA0;</mo><mi>m</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>s</mi><mi>l</mi><mi>o</mi><mi>p</mi><mi>e</mi><mo>&#xA0;</mo><mi>o</mi><mi>f</mi><mo>&#xA0;</mo><mi>t</mi><mi>h</mi><mi>e</mi><mo>&#xA0;</mo><mi>l</mi><mi>i</mi><mi>n</mi><mi>e</mi></math>


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Problem Details

The vapor pressure for pure water and pure acetone is measured as a function of temperature. In each case, a graph of the log of the vapor pressure versus 1/T is found to be a straight line. The slope of the line for water is -4895 K and the slope of the line for acetone is -3765 K. What is the ΔHvap of water?