As is observed in all forms of matter possessing adequate energy to undergo a transition in phase, an additional quantity of heat energy, known as the latent heat, must be emitted or absorbed by a substance in order to rearrange the molecular bonding pattern of the substance to that of its newly synthesizing phase. Within this experiment, the latent heat of vaporization of liquid nitrogen will be experimentally calculated for the liquid to gas transition of the chemical, with the goal of achieving minimal deviations in the results of the ten trial computations of latent heat. In theory, the average value for the latent heat of vaporization of liquid nitrogen within this experiment is expected to be 199.1 J/g with a standard deviation of 0 J/g, however, the actual results yielded an average latent heat of 195.4 J/g with a standard deviation of 10.42 J/g from this value. As discussed in the conclusion section, numerous errors of experimentation may have induced this rather significant level of deviation in results.
Theory:
As eluded to by the title of the experiment, this laboratory exercise will involve a thorough investigation of a specific thermodynamic property of liquid nitrogen, the substance’s latent heat of vaporization. As is dictated by the chemical’s name, liquid nitrogen is indeed representative of matter in a liquid state, with solids and gases constituting the other general phases of matter that can exist. To initiate a change in phase, a substance must first either emit or absorb energy in the form of heat, which will naturally result in a subsequent increase or decrease of the substance’s temperature. This process will proceed in an identical manner until the appropriate temperature at which the substance undergoes a phase change is reached. At this point, heat will continue to flow to or from the substance; however, the resulting change in temperature previously observed will not occur until the entirety of the substance has made a transition in phase. Chemically, this results from the energy that was previously being utilized to manipulate the temperature of the substance now becoming consumed to break or form the bonds associated with the varying phases of matter. This energy required for a phase transition is referred to as the latent heat, L, and can take the form of both the latent heat of vaporization (as seen in reactions involving vaporization and condensation), and the latent heat of fusion (associated with melting and freezing reactions). For this experiment, the value of L will be used to solely denote the latent heat of vaporization of liquid nitrogen. Physically, the latent heat represents the amount of energy in joules required to convert one gram of a substance to a differing phase of matter. Within this experiment, the latent heat of vaporization of liquid nitrogen will be quantified via usage of a resistor, a device that generates and transforms electrical energy of a known current and voltage into heat energy. As liquid nitrogen naturally vaporizes at 77° K, a temperature significantly cooler than that of the laboratory, the resistor will function to provide the liquid with a known input of energy, opposed to the unknown rate of energy transfer from the surrounding classroom, that can then be employed to calculate the latent heat. The methods involved in deriving the relation between the latent heat of vaporization and the heat transferred by the resistor will now be described.
Physically, the heat of matter can be quantified in terms of a substance’s mass and latent heat, as represented by the following equation: Q = mL, where Q is heat in Joules (J), m is mass in grams, and L is the latent heat in units of J/g. A transfer of any form of energy, (in this case the heat energy of the surrounding classroom and resistor to liquid nitrogen), is known as power, which is portrayed as the change in energy over a given period of time: P = ΔE / Δt, or in terms of heat energy, P = ΔQ / Δt. With the use of simple substitution, this equation can be manipulated to state that P = Δ(mL) / Δt, which can be further transformed, due to latent heat possessing a constant value, to read as follows: P = L [Δ(m) / Δt]. With this equation, the value of L can now be derived with the addition of one final bit of information, a known value for the power of the system. As noted above, the system of experimentation involves the transfer of heat from both the higher energy classroom and resistor to the lower energy liquid nitrogen. The exact amount of energy flowing from the classroom cannot be readily quantified, therefore, the only true means by which a value can be assigned to the power is through the known voltage and current of the resistor. Through the equation, Pr = IV (I being the current while V is the voltage) the heat energy transferred to the liquid nitrogen via resistor can now be calculated and substituted into the above equation relating the power and latent heat to yield: IV = L [Δ(m) / Δt2] = Pr To further simplify this equation, the value of Δ(m) / Δt2, bearing the units g/s, can be replaced with the variable, G, which possesses an identical set of units, producing the equation, IV = L * G. Finally, in terms of L, the seemingly complete equation for latent heat of vaporization reads as follows: L = IV / G. However, do to the fact that the heat transferred from the surrounding classroom to the liquid nitrogen cannot fully be insulated against, this heat will aid the resistor in vaporizing the liquid nitrogen and therefore must be recognized in the above equation. Denoting this mass of nitrogen vaporized by the classroom’s heat energy as B measured in g/s (derived from watts per unit latent heat), a new equation can be formulated and reads as follows: L = IV / G + B. As will be described in the procedure, by experimentally finding the value of B, this number can then be subtracted from the above equation in order to properly represent the latent heat of vaporization, the quantifiable energy entering the system from the resistor that is vaporizing a mass of liquid nitrogen. This final equation is as follows: L = IV / (G + B) – B.
As fully addressed in the procedure, this experiment involves ten separate calculations of the amount of time required to vaporize ten grams of liquid nitrogen, thus resulting in ten differing values of B and G +B, and consequently producing ten varying values of L. To determine the overall experimental accuracy, a standard deviation calculation will be performed, which will signify the average numerical deviation that exists between the mean value for all the values of L, and each L value individually. Mathematically, the standard deviation is represented as follows: σ = ? [?(ΔL)2 / n], where the standard deviation, σ, is equivalent to the square root of the summation of the square of the deviations of each individual L value from the mean value of L, divided by the sample size, n. The smaller the value of σ, the less the data is spread and therefore the greater the accuracy.
Procedure:
As direct, physical exposure to liquid nitrogen can result in frostbite, protective measures should first be taken before working with the substance. To promote maximum safety, utilize an apron and goggles at all times, and wear heavy gloves while pouring the liquid.Procure an insulated container for transport of the nitrogen, and with gloved hands, carefully dispense an appropriate quantity of the substance into the container. With the balance pre-set to counter a weight of 220 grams, gently pour the nitrogen out of the transport container into the insulated cup mounted upon the balance. Before pouring, ensure that the end segment of the resistor is not in direct contact with the surface of the cup, for when activated the device could singe and combust the paper constituting the cup. Continue to fill the cup until it possesses a combined mass with the liquid nitrogen that is slightly greater than 220 grams, causing the balance’s indicator to rise above the point of equalization.As the room’s heat slowly vaporizes the liquid nitrogen, observe the downward movement of the balance’s indicator as increasing quantities of nitrogen gas are released from the cup.
With a digital timer calibrated to cumulatively note the passage of time, start the timer at the exact moment when the indicator of the balance marks the equalization of the 220 gram counter weight with the insulated nitrogen-full cup. Simultaneously, set the balance to counter a mass of 210 grams, which will again result in the upward movement of the indicator until it has settled above the point of equalization.
With the timer continuously running, repeat this process of finding the equalization time in decreasing increments of 10 grams until ten separate times have been recorded and the combined mass of the cup and nitrogen has reached 120 grams. Calculate the individual lengths of time that transpired between each of the decreasing ten gram increments, and tabulate these values as Δt1.
Compute the rate of the change in mass by dividing each increment by it’s corresponding value of Δt1. The resulting value, quantified in g/s, will be denoted by B, and physically represents the rate at which the heat of the room is vaporizing the liquid nitrogen. For purposes of comparison, the assumption will be made that each successive value of B should in theory be identical, thus, each 10 gram decrease in mass will represent a single trial.
The above steps will now be repeated using the heat supplied by the active resistor in addition to the heat of the room to vaporize the liquid nitrogen. Switch the resistor to it’s active state and record the voltage and current of the flowing energy. Calculate the power of the resistor by finding the product of the voltage and current, and note this value.
Again, abiding by proper safety protocol, refill the insulated transport container with nitrogen and repeat the process of experimentation with the activated resistor adhering to the above guidelines. As before, tabulate the time passed between the vaporization of each ten gram interval, however, denote these values as Δt2.
In the same manner as previously employed, compute the rate of the change in mass, however, as this change is due to the heat transferred from both the room and the resistor, its value will be described with the notation of G + B. In order to find the mass of liquid nitrogen vaporized solely by the resistor, G, subtract the values of B from their corresponding G + B quantities for each gram interval. Finally, using the equation derived within the theory section, find the latent heat of vaporization for each trial.
To assess the relative accuracy of the data, perform a standard deviation computation for the ten values of the latent heat gathered through experimentation. The meaning of this statistic is fully discussed in the theory section.
Sample Calculations:
Resistor Power, Pr
Pr = IV
Pr = (0.835 amperes) * (30 volts)
Pr = 25.05 J/s
Rate of Change of Mass due to Background Heat, B
B = Δm / Δt
(B = P / L ? B = (J/s) / (J/g) ? B = g / s ? B = Δm / Δt )
B = (10 g) / (72.693 s)
B = 0.138 g/s
Rate of Change of Mass due to Resistor Heat, G
G = (G + B) – B
G = 0.257 g/s – 0.138 g/s
G = 0.119 g/s
Latent Heat of Vaporization, L
L = IV / (G + B) – B
L = (25.05 J/s) / (0.257 g/s – 0.138 g/s)
L = (25.05 J/s) / (0.119 g/s)
L = 210.5 J/g
Standard Deviation of L, σ
σ = ? [?(ΔL)2 / n]
σ = ? [1085 / 10]
σ = 10.42
Laverage = ?(L) / 10
Laverage = 195.4
195.4 ± 10.42
Conclusion:
As is universally observed in all forms of matter, the absorption or emission of heat energy will result in a direct temperature change by any substance. This property alone will enable a substance to obtain the proper level of energy, and thus the proper temperature, necessary to provoke a change in phase of matter. Chiefly among these phases are solids, possessing a dense packing of molecules, liquids, with an intermediate packing of molecules allowing shape variation, and gases, consisting of loosely packed molecules that permit both volume and shape change. Prior to a change in state of matter, a substance must continue to absorb or emit heat energy in order to fully convert it’s current state of molecular packing to that of the substance’s new phase. However, in contrast to the previous employment of heat energy to instigate only a direct change in temperature, this heat energy, known as latent heat, is utilized by the substance solely to break or form molecular bonds. Within this experiment, the latent heat of vaporization will be experimentally calculated for the liquid to gas transition of liquid nitrogen through a series of ten trials. The accuracy of these results will then be evaluated through a standard deviation calculation, with the goal of computing a relatively low value for this statistic that would imply a desired minimal variation in data. Although theoretically, the average value for the latent heat of vaporization of liquid nitrogen within this experiment is expected to be 199.1 J/g with a standard deviation of 0 J/g, the actual results yielded an experimental average latent heat of 195.4 J/g (derived from the ten trial latent heat values (in J/g) of 210.5, 212.3, 200.4, 195.7, 200.4, 185.6, 193.6, 193.2, 178.8, and 183.5), with the average distance from the mean value (the standard deviation) possessing a value of 10.42 J/g. Possible errors that may have contributed to this deviation include the effects of a solidifying mass on the external regions of the paper cup, and errors due to human judgment in both properly timing the precise moment of equivalence on the balance and the discrepancies in timing brought about by shifting the balance’s counter weights. The first of these areas of error involves the growing deposit of a solid (presumed to be ice brought about by the rapid cooling of the water vapor in the air by the significantly cooler nitrogen) that formed upon the outer layer of the insulated cup as the experiment progressed. Although minuscule in mass, the growing size of this deposit may have altered the presumably decreasing mass of the nitrogen containing cup, thus impacting the time required to vaporize the set mass of ten grams. As is common in situations involving a precise measurement of time, the judgment and human reaction rate associated with starting or stopping a timer, as with the stopping of the digital timer at the exact moment of mass equalization between the nitrogen cup and counter weight, is naturally imprecise and non-reproducible, therefore influencing the accuracy of this experiment’s Δt values. Similarly, with the unpredictable reaction time of humans, the shifting of the counter weights on the balance at the precise moment of equalization is nearly impossible. Therefore, if the stopping of the timer and the moving of the counter weights were not accomplished exactly in sync with one another, the values of Δt will again suffer a drop in accuracy, effecting the calculations of G and B and thus imparting flaws on the latent heat computations.
