The term ‘molar mass’ doubtlessly belongs to the group of scientific terms the knowledge of which is absolutely necessary for each educated student. In fact, some undergraduates consider that modern chemistry finds no application in different spheres of mundane life that have no strict interconnection with various scientific disciplines, such as modern biochemistry, colloid chemistry, ultrasonic sonochemistry, radiochemistry or stereochemistry. Without a doubt, this precipitate opinion is totally incorrect and, if it is allowed to say, even ignorant. Therefore, one of the primal purposes of every modern teacher is to demonstrate students that profound knowledge of chemistry is not only useful but also absolutely necessary in mundane life. Usually, pedagogues solve this important problem by using different assignments that allow students to understand and assimilate all the beauty and elegance of the modern chemical theory, such as various literary reports, essays about the history of chemistry and/or hermetic arts since its inception, personal essays about the main inventions and discoveries in the sphere of modern chemistry, etc. Naturally, this pedagogical approach has its own significant successes. In truth, an interesting, comprehensive and entertaining literary essay about some of these themes can have a greater educational impact on students than long and tedious hours of boring lectures. However, a modern teacher does not have to neglect a quite promising opportunity to combine practical and theoretical assignments in order to demonstrate undergraduates various examples of the application of modern chemistry from the practical point of view. Thereby, let us start with the definition of the terms ‘molar mass’ and ‘gas mixture’ with an eye to supply readers with primal chemical terminology before the practical tasks.
In chemistry, the molar mass (M) is a physical property, which is designated as the mass of a specific given substance divided by the amount of the substance. It also should be noted that by the term ‘substance’ we mean a specific chemical element or a chemical compound. Nowadays, the primal SI unit for the term ‘molar mass’ is kg/mol. However, this unit is not always suitable for our needs. For example, it is a quite sophisticated assignment to calculate the molar mass of the compound, which mass lies in the range of a few grams or even milligrams. Thereby, for practical and historical reasons the molar mass can be expressed in g/mol. Of course, the modern thesis methodology postulates that all terms and measurements in all scientifically oriented articles, reports and official documents have to be expressed in the appropriate SI units. However, one should not be frightened to use ‘g/mol’ units in order to simplify oversophisticated calculations because all these units correctly express the physical sense of the term ‘molar mass’.
From the practical standpoint the molar mass is a ratio of the mass of material to the number of moles of the substance. For individual chemical elements, the molar mass is the mass of one mole of the individual atoms (ions) of the element. In this case, the molar mass of the element, which is expressed in g/mol, is numerically equal to the molecular mass of the element, expressed in a. e. m. (atomic mass units). However, students have to understand clearly that there exists a significant difference between the molar mass and molecular weight. One should always remember that these units are equal only numerically and that they considerably differ in dimensions. The molar mass is also closely associated with the term ‘relative molar mass’ (Mr), the elder term formula weight (F.W.). The molecular weight (M.W.) and the formula weight (F.W.) are elder terms for what is now more rightly called the relative molar mass (Mr). This is a dimensionless quantity (a pure number, without units) equal to the molar mass that is divided by the molar mass constant.
From the scientific point of view, the air is a natural mixture of gases (mainly nitrogen and oxygen - in the amount of 98-99%, as well as argon, carbon dioxide, water vapor, hydrogen), which forms the Earth's atmosphere. Naturally, the composition of the air may significantly vary according to the geographical location of the territory. For example, in major cities, the carbon dioxide content is higher than in the forests due to the massive air pollution. In fact, in the different corners of the globe, the air composition may vary within 1-3% of each gas. Hence, the average molar mass of air can also differ in diverse regions of the planet according to the physical conditions of each single region (altitude, latitude, temperature, relative and absolute humidity of the air, etc.). Nevertheless, in a standard virtual experiment, which is aimed at determination of the average molar mass of air students can use the common proportion of gases, in order to achieve acceptable accuracy. The average molar mass of the gas mixture can be calculated using the molar masses of the single components of the mixture of gases and their volume fractions.
As it was mentioned earlier the average molar mass of every specific gas mixture can be identified by examining the proportions of the molar masses of its single components. Therefore, a circumspect pedagogue can use two completely different approaches to the topic ‘the molar mass of air ’: pure theoretical lectures together with various virtual experiments or practical experiments. Both of these methods can lead to the quite satisfactory results from the pedagogical point of view. The theoretical method has a wide range of different special advantages. It is absolutely safe for all participants of the experiment regardless of their previously obtained laboratory experience, demonstrative and time-saving. However, the practical educational technique is much better in terms of clarity and intelligibility because it allows undergraduates to take part in the experiment, obtain priceless practical experience and understand all significant aspects, and important nuances of the experiment. Therefore, one can achieve the best educational results combining these educational techniques with an eye to examining the problem from all possible sides: both theoretical and practical.
Firstly, we have to determine the allowable calculation error. If we do not need high precision in our computations, we can limit elements of the study to only three of the most "weighty" elements of the air: the nitrogen gas, oxygen and argon. Thereby, we can use the "rounded" values of their concentrations in order to achieve desirable simplicity and visibility of our calculations of the average molar mass of air. In addition, we can verify all results, which have been obtained during our experiments, using the standard tables that demonstrate students the ratio of various gases that form the mixture, which is commonly known as the ‘air’. During the essay editing we can also compare the results of our calculations in order to fix all gross mistakes, identify errors in computations and emphasize the most significant key-points of our virtual experiment. Naturally, if we need results that are more precise, we can use in the computations other air gases, such as carbon dioxide, argon, neon, xenon, etc. Secondly, we should determine the molecular weights of these components and their concentration in the air mass. Here is a concise list of these characteristics that are necessary for our virtual experiments:
With an eye to significantly facilitate our calculations, we can round the concentration values: nitrogen up to 76%; oxygen up to 23% and argon up to 1.3%. Thirdly, we have to perform elementary computations in order to identify the average molar mass of air. We have to multiply the molecular weight of each single gas and its mass concentration and then add the results. Here is a primitive equation that describes this process: 28x0.76 + 32x0.23 + 40x0, 013 = 29.16 g/mol. As we can see, the results, which were obtained during our computations, are very close to the value of the average molar mass of air that is listed in different chemical compendiums and directories: 28.98 g/mol. In addition, we can interpret all discrepancies as the results of previously performed rounding. Finally, we have to compose a standard research proposal, which contains all important details about all stages of our virtual experiment, results that were received during our computations, conclusions and interpretations of the received data.
Alternatively, we can determine the average molar mass of air using a classical and quite simple laboratory experiment. For this experiment, we will need accurate laboratory scales, round-bottomed flask with ground joint and crane, the standard vacuum pump, the pressure gauge with two valves and connecting hoses, thermometer. Firstly, measure the mass of the flask, which, obviously, contains the air inside. Record the obtained results. Secondly, evacuate the air from the flask using the pump. Wait a few minutes so that the air in the flask will be heated to room temperature. Record the pressure gauge and thermometer. Thirdly, closing the valve on the bulb, disconnect the hose from the gauge and weigh the flask with the new (reduced) amount of air. Record the obtained results. Finally, double-check all results with an eye to eschew undesirable errors in further computations. Using the ideal gas law equation and our results, we can calculate the average molar mass of air. Due to our experiment, we know both the change in air pressure (ΔP) and the change of the air mass (ΔM). According to the equation: m = ∆MRT/∆PV. After a series of simple calculations, we can determine the average molar mass of air. Naturally, your results may differ from those that are listed in various directories. In this case, you should examine all stages of your experiment with an eye to finding all methodological errors or possible mistakes in the previously performed calculations.
In fact, Antoine-Laurent de Lavoisier was the first scientists who has approached the understanding of the composition of air. Nowadays, virtually all historical oriented thesis examples, which are dedicated to this theme, acknowledge his primacy in this sphere of science. Lavoisier proved that the process of burning the substance is not released from the compound. Moreover, he demonstrated that during the burning process some specific component of the air associated with the given substance. This discovery paved the way for future Lavoisier’s success. Through analysis and synthesis, he showed that air is a mixture of two gases: the first of them is the gas that maintains the burning process ("healthy (salubre) air’) and the second inactive gas, which does not take part in this chemical reaction (‘unhealthy (moffett) air’). Nowadays, we call these gases oxygen ("healthy (salubre) air’) and nitrogen (‘unhealthy (moffett) air’). Therefore, we can admit that Antoine-Laurent de Lavoisier is the first chemist who has succeeded in identifying a weight ratio of the air gases. Obviously, practically all modern methods, which are aimed at identification and verification of the molar mass of air, are based on the principles and theories that significantly differ from those chemical theories that were used by Lavoisier. Nevertheless, his experiments and postulates were of extremely high priority for chemical science of his time.