To determine the empirical formula of a compound from its complace by mass. To derive the molecular formula of a compound from its empirical formula.

You are watching: The total number of atoms in a molecule of sucrose


When a new steustatiushistory.orgical compound, such as a potential brand-new pharmaceutical, is synthesized in the laboratory or isolated from a natural resource, steustatiushistory.orgists recognize its elemental complace, its empirical formula, and also its framework to understand its properties. This area concentrates on exactly how to recognize the empirical formula of a compound and then use it to identify the molecular formula if the molar mass of the compound is recognized.


Formula and also Molecular Weights

The formula weight of a substance is the sum of the atomic weights of each atom in its steustatiushistory.orgical formula. For instance, water (H2O) has actually a formula weight of:

<2 imes(1.0079;amu) + 1 imes (15.9994 ;amu) = 18.01528 ;amu>

If a substance exists as discrete molecules (as via atoms that are steustatiushistory.orgically bonded together) then the steustatiushistory.orgical formula is the molecular formula, and also the formula weight is the molecular weight. For example, carbon, hydrogen and also oxygen deserve to steustatiushistory.orgically bond to create a molecule of the sugar glucose via the steustatiushistory.orgical and also molecular formula of C6H12O6. The formula weight and also the molecular weight of glucose is thus:

<6 imes(12; amu) + 12 imes(1.00794; amu) + 6 imes(15.9994; amu) = 180.0 ;amu>

Ionic substances are not steustatiushistory.orgically bonded and also carry out not exist as discrete molecules. However, they execute associate in discrete ratios of ions. Hence, we have the right to describe their formula weights, however not their molecular weights. Table salt ((ceNaCl)), for instance, has actually a formula weight of:

<23.0; amu + 35.5 ;amu = 58.5 ;amu>


Percentage Composition from Formulas

In some forms of analyses of it is crucial to know the percentage by mass of each kind of facet in a compound. The legislation of definite prosections claims that a steustatiushistory.orgical compound always has the very same propercent of elements by mass; that is, the percent composition—the percent of each element current in a pure substance—is consistent (although tbelow are exceptions to this law). Take for example methane ((CH_4)) through a Formula and molecular weight:

<1 imes (12.011 ;amu) + 4 imes (1.008) = 16.043 ;amu>

the relative (mass) percentperiods of carbon and also hydrogen are

<\%C = dfrac1 imes (12.011; amu)16.043 amu = 0.749 = 74.9\%>

<\%H = dfrac4 imes (1.008 ;amu)16.043; amu = 0.251 = 25.1\%>

A more complicated example is sucrose (table sugar), which is 42.11% carbon, 6.48% hydrogen, and also 51.41% oxygen by mass. This indicates that 100.00 g of sucincreased constantly includes 42.11 g of carbon, 6.48 g of hydrogen, and also 51.41 g of oxygen. First the molecular formula of sucincreased (C12H22O11) is provided to calculate the mass percent of the component elements; the mass percentage can then be supplied to identify an empirical formula.

According to its molecular formula, each molecule of succlimbed contains 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms. A mole of succlimbed molecules therefore contains 12 mol of carbon atoms, 22 mol of hydrogen atoms, and also 11 mol of oxygen atoms. This information deserve to be used to calculate the mass of each facet in 1 mol of sucincreased, which offers the molar mass of sucincreased. These masses deserve to then be offered to calculate the percent composition of succlimbed. To 3 decimal places, the calculations are the following:

< ext mass of C/mol of sucrose = 12 , mol , C imes 12.011 , g , C over 1 , mol , C = 144.132 , g , C label3.1.1a>

< message mass of H/mol of sucrose = 22 , mol , H imes 1.008 , g , H over 1 , mol , H = 22.176 , g , H label3.1.1b>

< ext mass of O/mol of sucrose = 11 , mol , O imes 15.999 , g , O over 1 , mol , O = 175.989 , g , O label3.1.1c>

Hence 1 mol of sucincreased has a mass of 342.297 g; note that even more than fifty percent of the mass (175.989 g) is oxygen, and also nearly half of the mass (144.132 g) is carbon.

The mass portion of each facet in succlimbed is the mass of the element existing in 1 mol of succlimbed separated by the molar mass of sucincreased, multiplied by 100 to offer a portion. The outcome is displayed to two decimal places:

< message mass % C in Sucrose = ext mass of C/mol sucrose over ext molar mass of sucrose imes 100 = 144.132 , g , C over 342.297 , g/mol imes 100 = 42.11 \% >

< ext mass % H in Sucrose = message mass of H/mol sucrose over message molar mass of sucrose imes 100 = 22.176 , g , H over 342.297 , g/mol imes 100 = 6.48 \% >

< message mass % O in Sucrose = message mass of O/mol sucrose over message molar mass of sucrose imes 100 = 175.989 , g , O over 342.297 , g/mol imes 100 = 51.41 \% >

This have the right to be checked by verifying that the amount of the percenteras of all the facets in the compound is 100%:

< 42.11\% + 6.48\% + 51.41\% = 100.00\%>

If the sum is not 100%, an error has actually been made in calculations. (Rounding to the correct number of decimal locations can, yet, reason the full to be slightly different from 100%.) Thus 100.00 g of sucrose contains 42.11 g of carbon, 6.48 g of hydrogen, and 51.41 g of oxygen; to 2 decimal locations, the percent complace of succlimbed is indeed 42.11% carbon, 6.48% hydrogen, and 51.41% oxygen.

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Figure (PageIndex1): Percent and also absolute complace of sucrose

It is additionally possible to calculate mass percentages utilizing atomic masses and molecular masses, through atomic mass systems. Since the answer is a ratio, expressed as a portion, the devices of mass cancel whether they are grams (using molar masses) or atomic mass devices (using atomic and also molecular masses).


Example (PageIndex1): NutraSweet

Aspartame is the synthetic sweetener offered as NutraSweet and also Equal. Its molecular formula is (ceC14H18N2O5).

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Molecular Structure of Aspartame. (CC BY-NC-SA 3.0; anonymous) Calculate the mass percentage of each aspect in aspartame. Calculate the mass of carbon in a 1.00 g packet of Equal, assuming it is pure aspartame.

Given: molecular formula and mass of sample

Asked for: mass percentage of all aspects and also mass of one aspect in sample

Strategy:

Use atomic masses from the periodic table to calculate the molar mass of aspartame. Divide the mass of each aspect by the molar mass of aspartame; then multiply by 100 to achieve percenteras. To find the mass of an aspect had in a offered mass of aspartame, multiply the mass of aspartame by the mass portion of that aspect, expressed as a decimal.

Solution:

a.

A We calculate the mass of each facet in 1 mol of aspartame and also the molar mass of aspartame, here to 3 decimal places:

< 14 ,C (14 , mol , C)(12.011 , g/mol , C) = 168.154 , g>

< 18 ,H (18 , mol , H)(1.008 , g/mol , H) = 18.114 , g>

< 2 ,N (2 , mol , N)(14.007 , g/mol , N) = 28.014 , g>

< +5 ,O (5 , mol , O)(15.999 , g/mol , O) = 79.995 , g>

Therefore more than fifty percent the mass of 1 mol of aspartame (294.277 g) is carbon (168.154 g).

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B To calculate the mass percentage of each facet, we divide the mass of each facet in the compound by the molar mass of aspartame and also then multiply by 100 to attain percentperiods, here reported to 2 decimal places:

< mass \% , C = 168.154 , g , C over 294.277 , g , aspartame imes 100 = 57.14 \% C>

< mass \% , H = 18.114 , g , H over 294.277 , g , aspartame imes 100 = 6.16 \% H>

< mass \% , N = 28.014 , g , N over 294.277 , g , aspartame imes 100 = 9.52 \% >

< mass \% , O = 79.995 , g , O over 294.277 , g , aspartame imes 100 = 27.18 \% >

As a check, we have the right to include the percentages together:

< 57.14\% + 6.16\% + 9.52\% + 27.18\% = 100.00\% >

If you achieve a total that differs from 100% by even more than about ±1%, tright here must be an error somewhere in the calculation.