Consider a substance X with a Hvap = 20.3 kJ/mol and Hfus = 9.0 kJ/mol. The boil
ID: 510143 • Letter: C
Question
Consider a substance X with a Hvap = 20.3 kJ/mol and Hfus = 9.0 kJ/mol. The boiling point, freezing point, and heat capacities of both the solid and liquid X are identical to those of water. If you placed one beaker containing 50 g of X at 10°C and another beaker with 50 g of H2O at -10°C on a hot plate and started heating them, which material would reach the boiling point
first? Assume the molar mass of X is similar to that of water.
a. Which of the materials from part a., X or H2O, would completely boil away first? b. On a piece of graph paper, draw the heating curve for H2O and X. How do the heating
curves reflect your answers from parts a and b?
Explanation / Answer
a. If you placed one beaker containing 50 g of X at -10°C and another beaker with 50 g of H2O at -10°C on a hot plate and started heating them, which material would reach the boiling point first?
X (Hfus = 9.0 kJ/mol and Hvap = 20.3 kJ/mol) with the values for water, which are Hfus = 6.01 kJ/mol and Hvap = 40.7 kJ/mol.
Comparing values shows that Hfus is 1.5 times larger for substance X, and Hvap is 2.0 times larger for H2O. Heating the substance, or water, from -10°C to the boiling point is a three step process.
Step 1 is to heat the solid from -10°C to 0°C, the freezing point.
The heat required for this step is equal to mass x specific heat capacity x temperature change.
Step 2 is to melt the solid to liquid at 0°C.
The heat required for this step is equal to moles x Hfus.
Step 3 is to heat the liquid from 0°C to 100°C.
The heat required for this step is equal to mass x specific heat capacity x temperature change.
a. Since the masses, heat capacities, and temperature changes for water and for substance X are all equal, the heat required for step 1 and step 3 are the same for both. Since Hfus is larger for substance X (per mole), step 2 will require more heat for substance X, and thus take longer.
Therefore, H2O will reach the boiling point first.
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b. To completely boil away the substance, an additional step is required.
Step 4 is to boil the liquid to vapor at 100°C. The heat required for this step is equal to moles x Hvap.
Since the Hvap values are much larger than the Hfus values, step 4 will require much more heat than step 2 for both substance X and H2O.
Since Hvap is smaller for substance X (per mole),
step 4 will require less heat for substance X, and thus take less time.
The total heat required for the four steps is directly proportional to the time it would take to completely boil away the substance.
Steps 1 and 3 are the same for both.
Step 2 takes 1.5 times as long for substance X, but step 4 takes 2.0 times as long for water.
Since step 4 requires the most heat, water will require more time to complete this step,
so substance X will boil away first.