Thus more than half the mass of 1 mol of aspartame (294.277 g) is carbon (168.154 g). A We begin by dividing the mass of each element in 100.0 g of caffeine (49.18 g of carbon, 5.39 g of hydrogen, 28.65 g of nitrogen, 16.68 g of oxygen) by its molar mass. Each glucose contains six CH2O formula units, which gives a molecular formula for glucose of (CH2O)6, which is more commonly written as C6H12O6. Because the mold was a member of the Penicillium family (named for their pencil-shaped branches under the microscope) (part (b) in Figure \(\PageIndex{2}\)), Fleming called the active ingredient in the broth penicillin. 9.0\; \cancel{g\; S}\dfrac{1\; mol\; S}{32.065\; \cancel{g\; S}} &=0.28\; mol\; S \\ & & \\ Atomic Mass: 12.0107 . Calculate the molar mass of aspartame.b. Table salt (\(\ce{NaCl}\)), for example, has a formula weight of: \[23.0\; amu + 35.5 \;amu = 58.5 \;amu \nonumber \], Molar Masses of Compounds, YouTube: Molar Masses of Compounds(opens in new window) [youtu.be]. The molecular formula of aspartame is C14H18N205. B Obtain the relative numbers of atoms of each element in the compound by dividing the number of moles of each element in the 100 g sample by the number of moles of the element present in the smallest amount. Just as in Example 6, it is reasonable to assume that such small deviations from integral values are due to minor experimental errors, so round to the nearest integer. We can use this information to calculate the mass of each element in 1 mol of sucrose, which will give us the molar mass of sucrose. Like Freon-11, Freon-114 is a commonly used refrigerant that has been implicated in the destruction of the ozone layer. No; rounding errors in the calculations as well as experimental errors in the data can result in nonintegral ratios. A more complex example is sucrose (table sugar), which is 42.11% carbon, 6.48% hydrogen, and 51.41% oxygen by mass. Calculate the mass in grams of 1.56 mol apartame c. 17.9\; \cancel{g\; O}\dfrac{1\; mol\; O}{15.999\; \cancel{g\; O}} &=1.12\; mol\; O This information can be used to calculate the mass of each element in 1 mol of sucrose, which gives the molar mass of sucrose. Do not assume that the missing mass is always due to oxygen. See Answer moles\; O & =53.79\; \cancel{g\; O}\dfrac{1\; mol\; C}{15.9994\; \cancel{gO}} & = 3.362\; mol\; O C 14 H 18 N 2 O 5 . Step by step Solved in 2 steps with 2 images See solution Check out a sample Q&A here Knowledge Booster Learn more about Need a deep-dive on the concept behind this application? (Rounding to the correct number of decimal places can, however, cause the total to be slightly different from 100%.) Legal. Using the chemical formula of the compound and the periodic table of elements, we can add up the atomic weights and calculate molecular weight of the substance. a. Calculate the molar mass of aspartame. Finally, in 1940, two chemists at Oxford University, Howard Florey (18981968) and Ernst Chain (19061979), were able to isolate an active product, which they called penicillin G. Within three years, penicillin G was in widespread use for treating pneumonia, gangrene, gonorrhea, and other diseases, and its use greatly increased the survival rate of wounded soldiers in World War II. The results will be the subscripts of the elements in the empirical formula. The formula mass is calculated as follows: \[ 4C \, \, \, ( 4 \, atoms \, C) (12.011 \, g/ atom \, C) = 48.044 \, g\nonumber \], \[ 5H \, \, \, ( 5 \, atoms \, H ) (1.0079 \, g/ atom \, H) = 5.0395 \, g \nonumber \], \[ 2N \, \, \, (2 \, atoms \, N) (14.0067 \, g/ atom \, N) = 28.0134 \, g \nonumber \], \[ +1O \, \, \, (1 \, atom \, O) (15.9994 \, g/ atom \, O) = 15.9994 \, g \nonumber \], \[ C_4H_5N_2O \, \, \, \, \text {formula mass of caffeine} = 97.096 \, g\nonumber \], Dividing the measured molar mass of caffeine (196 g/mol) by the calculated formula mass gives, \[ {196 g/mol \over 97.096 g/C_4H_5N_2O } = 2.02 \approx 2\, C_4H_5N_2O \, \text {empirical formula units}\nonumber \]. They discovered that a typical sample of penicillin G contains 53.9% carbon, 4.8% hydrogen, 7.9% nitrogen, 9.0% sulfur, and 6.5% sodium by mass. A A 100 g sample of calcium phosphate contains 38.77 g of calcium, 19.97 g of phosphorus, and 41.27 g of oxygen. mass of Aspartame = 10.0 g. Molar mass of Aspartame = 294 g/mol. Because there are two phosphorus atoms in the empirical formula, two phosphate ions must be present. The molar mass of salicylic acid is 138.12 g/mol. When a new chemical compound, such as a potential new pharmaceutical, is synthesized in the laboratory or isolated from a natural source, chemists determine its elemental composition, its empirical formula, and its structure to understand its properties. Once again, we find the subscripts of the elements in the empirical formula by dividing the number of moles of each element by the number of moles of the element present in the smallest amount: \( \begin{matrix} The empirical formula of penicillin G is therefore C16H17N2NaO4S. Thus naphthalene contains a 1.25:1 ratio of moles of carbon to moles of hydrogen: C1.25H1.0. chemistry. Complete combustion of a 20.10 mg sample of naphthalene in oxygen yielded 69.00 mg of CO2 and 11.30 mg of H2O. c. How many molecules are in 5 mg of aspartame? Once again, the subscripts of the elements in the empirical formula are found by dividing the number of moles of each element by the number of moles of the element present in the smallest amount: \[ C: {3.304 \over 3.304} = 1.000 \, \, \, \, H: {6.53 \over 3.304} = 1.98 \, \, \, \, O: {3.362 \over 3.304} = 1.018 \nonumber \]. B Divide the mass of each element by the molar mass of aspartame; then multiply by 100 to obtain percentages. If the ratios are not integers, multiply all subscripts by the same number to give integral values. moles\; C &=39.68\; \cancel{g\; C}\dfrac{1\; mol\; C}{12.011\; \cancel{gC}} & = 3.304\; mol\; C \\ & \\ mass\; \%\; H\; in\; sucrose & =\dfrac{mass\; of\; H/mol\; sucrose}{molar\; mass\; of\; sucrose}\times 100 & =\dfrac{22.176\; g\; H}{342.297\; g/mol}\times 100 & =6.48 \%\\ ), { "3.01:_Chemical_Equations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.02:_Some_Simple_Patterns_of_Chemical_Reactivity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.03:_Formula_Masses" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.04:_Avogadro\'s_Number_and_the_Mole" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass230_0.b__1]()", "3.05:_Empirical_Formulas_from_Analysis" : 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C The mass of carbon in 1.00 g of aspartame is calculated as follows: \[ \text {mass of C} = 1.00 \, g \, aspartame \times {57.14 \, g \, C \over 100 \, g \, aspartame } = 0.571 \, g \, C \nonumber \]. Xylene, an organic compound that is a major component of many gasoline blends, contains carbon and hydrogen only. To determine the empirical formula from the mass percentages of the elements in a compound such as penicillin G, we need to convert the mass percentages to relative numbers of atoms. Use atomic masses from the periodic table to calculate the molar mass of aspartame. 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