Heat of Fusion for Ice

HEAT OF FUSION FOR ICE | 125 Heat of Fusion for Ice OBJECTIVES: • Become familiar with the thermodynamics of phase changes for a pure substance • Pra...
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HEAT OF FUSION FOR ICE | 125

Heat of Fusion for Ice OBJECTIVES: • Become familiar with the thermodynamics of phase changes for a pure substance • Practice mass and temperature measurement techniques • Calculate the molar enthalpy of fusion for ice DISCUSSION: Melting and freezing behavior are among the characteristic properties that give a pure substance its unique identity. As energy is added, pure solid water (ice) at 0 °C changes to liquid water, without a temperature change. In this lab exercise, you and a partner will determine the energy (in joules) required to melt one gram of ice. You will then determine the molar heat of fusion for ice (in kJ/mol). Excess ice will be added to warm water, at a known temperature, in a Styrofoam cup calorimeter. The warm water will be cooled to temperature near 0 °C by the ice. The energy required to melt the ice is removed from the warm water as it cools. To calculate the amount of heat flow from the water, use the relationship: q = CP ⋅ m ⋅ ² T (1) where q stands for heat flow (in J), CP is the specific heat (in J/g·°C), m is mass in grams, and ∆T is the change in temperature (in °C). For liquid water, CP = 4.18 J/g·°C. PROCEDURE: 1. Support a Styrofoam cup in a 250-mL beaker. 2. Use a utility clamp and a slit stopper to suspend a thermometer or thermocouple on a ring stand. Position the temperature probe above the Styrofoam cup. 3. Heat 250 mL of water to about 60 °C. Obtain 7 or 8 large ice cubes, and keep them ready. Use a graduated cylinder to measure 100 mL of the hot water into the cup. Record this as V1. 4. Lower the temperature probe into the hot water (to about 1 cm from the bottom of the cup). 5. Wait for the temperature reading to reach a maximum (it will take some time for the probe to reach the temperature of the water). Record this initial reading as T1 on your data sheet. 6. Remove excess liquid from the ice by shaking or patting with a paper towel. Add the ice to the hot water. Begin recording the temperature reading every 20 s. 7. To prevent the creation of temperature and density gradients in the cup, use a clean stirring rod to keep the ice and water well mixed. As the ice melts, add more large cubes to keep the mixture full of ice. 8. When the temperature seems to stabilize (probably at around 4°C), quickly use tongs to remove the unmelted ice. Continue stirring and recording the temperature until the reading reaches a minimum, then begins to rise. Record this minimum reading as T2 on your data sheet. 9. Measure the volume of water in the cup to the full precision of a 100-mL graduated cylinder. Record this as V2.

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DATA ANALYSIS 1. Find the temperature changes of the hot water, ∆Thot, and the melt water, ∆Tcold. Assume that the ice was initially at 0 °C, so you can neglect any heat required to warm the ice to its melting point. 2. Calculate the mass of hot water initially present, using the measured volume (V1) and the density of water at 60 °C (ρ 60 = 0.98 g/mL). 3. Calculate the mass of melt water, using the measured volume (V2) and the density of water at 4 °C (ρ 4 = 1.00 g/mL), and then subtracting the mass of hot water calculated above. 4. Use Equation (1) from the Discussion section to calculate the heat lost by the hot water. Note that because the hot water cools, it has a negative ∆T value and thus a negative q value as well. Repeat the calculation for the heat gained by the cold melt water. 5. Now apply the first law of thermodynamics. Assuming that the calorimeter loses no heat to the surroundings, and that the work flow term is too small to be significant, we have: qhot + qcold + q fusion = 0 (2) That is, assume that all of the heat lost by the hot water in your calorimeter was taken up by the warming melt water or the melting ice. 6. Use your value of qfusion calculated above, and the molar mass of water to find the molar enthalpy of fusion for ice. Express ∆Hfusion in kJ/mol units. 7. The molar enthalpy of fusion for ice at 0 °C has an accepted value of +6.01 kJ/mol. Calculate a percent error value to compare your experimental result with the accepted value.

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Prelaboratory Assignment FOR FULL CREDIT, SHOW DETAILED CALCULATION SETUPS. REMEMBER TO FOLLOW THE SIGNIFICANT FIGURES CONVENTION, AND TO SHOW MEASUREMENT UNITS FOR EACH QUANTITY. 1. Define “heat of fusion”.

2. When 27.2 g of solid A, at its melting point of 34.0 °C, was added to 62.7 g of liquid A at 51.2 °C, the mixture cooled to 35.0 °C, with no solid remaining. Given the specific heat of liquid A (CP = 0.798 J/g·°C), find the heat of fusion per gram of solid A. Step 1 A→ (s) 34.0 °C

→ 34.0°C

SKETCH

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Data Sheet RECORD TEMPERATURES TO THE THERMOMETER’S FULL AVAILABLE PRECISION. time (s)

T (°C)

time (s)

T (°C)

time (s)

0

180

360

20

200

380

40

220

400

60

240

420

80

260

440

100

280

460

120

300

480

140

320

500

160

340

520

Hot water volume, V1 Hot water initial temperature, T1

mL °C

T (°C)

Final water volume, V2 Final water temperature, T2

mL °C

Calculation Results SHOW COMPLETE CALCULATION SETUPS ON THE BACK OF THIS SHEET. FOLLOW THE SIGNIFICANT FIGURES CONVENTION AND SHOW UNITS FOR ALL QUANTITIES.

Hot water mass

g

Total water mass

g

Melt water mass

g

Hot water temperature change

°C

Melt water temperature change

°C

Heat lost by hot water

J

Heat gained by melt water

J

∆Hfus

kJ/mol

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Calculations Hot water mass: m hot = V1·ρ 

Total water mass: m total = V2·ρ 4

Melt water mass: m melt = m total – m hot

Hot water temperature change: ∆T hot = T2 – T1

Melt water temperature change: ∆T melt = T2 – 0.0 °C

Heat lost by hot water: q hot = CP · m hot · ∆T hot

Heat gained by melt water: q melt = CP · m melt · ∆T melt

Heat absorbed by melting ice: q fusion = –(q hot + q melt)

Heat absorbed per mole: ² H fus =

q fusion molesmelt

% difference from accepted value:

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Postlaboratory Assignment FOR FULL CREDIT, SHOW DETAILS OF EACH CALCULATION BELOW. USE MORE PAPER IF NEEDED. 1. If all the ice were to melt just as the temperature reached 3.0 °C, would this produce an error in your experimental values? Explain your reasoning.

2. A 125-g metal block at a temperature of 93.2 °C was immersed in 100. g of water at 18.3 °C. Given the specific heat of the metal (CP = 0.900 J/g·°C), find the final temperature of the block and the water.

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