Calculations weighted-average atomic masses

Using the data given by the graph, calculate the weighted average atomic mass of element X. Identify the unknown element. 

If you obtain the isotopic abundance of an element from mass spectrometer data or a table, you can calculate the average atomic mass of the element. You do this by calculating the weighted average of each isotope s mass. A weighted average takes into account not only the values associated with a set of data, but also the abundance or importance of each value. 

Explain why you use a weighted average, based on the masses and abundances of the isotopes, to calculate the average atomic mass of an element. 

Calculate the average atomic mass (the atomic weight) of magnesium from these data. 

If you know the abundance of each isotope, you can calculate the average atomic mass of an element. For example, the average atomic mass of native copper is a weighted average of the atomic masses of two isotopes, shown in Figure 5. The following sample problem shows how this calculation is made from data for the abundance of each of native copper s isotopes. 

Calculating the Weighted Average Atomic Mass of Chlorine... 

To determine the weighted average atomic mass of chlorine, the mass contribution of each of the two isotopes is calculated, and then those two values are added together. 

The weighted-average atomic mass takes into account the fact that about 76% of the chlorine atoms are of the lighter isotope, Cl-35, and about 24%, the heavier. Here is how the atomic mass of chlorine is calculated, taking into account the fact that it is composed of two isotopes ... 

Consider a hypothetical element, X, that has three isotopes. Calculate the weighted-average atomic mass of the element from the following data. 

Background Most elements in nature occur as a mixture of isotopes. The weighted average atomic mass of an element can be determined from the atomic mass and the relative abundance of each isotope. In this activity, you will model the isotopes of the imaginary element "Snackium." The measurements you make will be used to calculate a weighted average mass that represents the average atomic mass of "Snackium."... 

Calculate Use the isotopic percent abimdance of the snack pieces and the mass to calculate the weighted average atomic mass for your element Snackium. ... 

Calculate the weighted average atomic mass of zirconium. 

SECTION Z4 The atomic mass scale is defined by assigning a mass of exactly 12 amu to a atom. The atomic weight (average atomic mass) of an element can be calculated from the relative abundances and masses of that elements isotopes. The mass spectrometer provides the most direct and accurate means of experimentally measuring atomic (and molecular) weights. 

Only two isotopes of copper occur naturally, Cu (atomic mass = 62.9296 amu abundance 69.17%) and (atomic mass = 64.9278 amu abundance 30.83%). Calculate the atomic weight (average atomic mass) of copper. 

In Table 8.18, mx, is the exact mass of the isotope of X that differs by i integer mass units from m, and is the corresponding relative abundance. Isotopes of relative abundance lower than 0.001 are neglected. Suchcases are with mn i = 2.014102 Da, j = 0.00015 and with = 35.967079 Da, and = 0.00020. A more extensive list of exact masses and isotope distribution for most elements is available online, e.g. [288], as well as in many standard reference books. The exact isotope masses are weighted by their intensities to calculate the average atom mass of a chemical element ... 

Naturally occurring chlorine is 75.78% C1, which has an atomic mass of 34.%9 amu, and 24.22% Cl, which has an atomic mass of 36.966 amu. Calculate the average atomic mass (that is, the atomic weight) of chlorine. 

Sometimes a qualitative understanding of the relationship between isotopic masses, percent isotopic abundances, and weighted-average atomic mass is all that we need, and no calculation is necessary, as illustrated in Example 2-5. Example 2-6 and the accompanying Practice Examples provide additional applications of equation (2.3). 

PRACTICE EXAMPLE A The masses and percent isotopic abundances of the three naturally occurring isotopes of silicon are Si, 27.9769265325 u, 92.223% Si, 28.976494700 u, 4.685% °Si, 29.973377017 u, 3.092%. Calculate the weighted-average atomic mass of silicon. 

Two forms of the same element are called isotopes. The isotopes of an element have the same atomic number but have different atomic masses. Iron has several isotopes that, when weighted by their naturally occurring abundance, gives an average mass of 55.845 amu. A simple example would be an element with only two isotopes, one with a mass of 10 amu, the other of 12 amu. If the isotopes were equally common, then the average atomic mass for that element would be 11. If 90% of the element occurred naturally as the isotope with a mass of 10 amu, then the average atomic mass would be 10.2, as calculated below ... 

If the mass percent of the isotopes of an element is known, then the average atomic weight can be calculated. For example, naturally occurring bromine has one isotope with a mass of 78.918 amu and makes up 50.69% of a bromine sample. Another isotope has a mass of 80.916 amu and an abundance of 49.31%. The average atomic mass of bromine equals the percent abundance of the first isotope divided by 100 times the mass percent of the isotope plus the percent abundance of the second isotope divided by 100 times the mass percent abundance of the second isotope (.5096) (78.918) plus (.4931) (80.916) equals 79.90, the average atomic mass of bromine. 

The molecular mass of a compound is calculated by adding up the atomic masses of the constituent elements. Those masses are the average atomic masses, which are the weighted masses of the various isotopic forms of the elements involved. The nuclidic molecular mass may be defined for a molecule made up of particular nuclides by adding nuclidic atomic masses in the same way that the usual molecular mass is computed from the atomic... 

Use the data you have just gathered to calculate the mass of the pennies, using a weighted average. This represents the "average atomic mass" of centium. 

Explain why you need to use a weighted average to calculate average atomic mass. 

Just as the atomic weight of an element is the average atomic mass for one atom of the naturally occurring element, expressed in atomic mass units, the formula weight of a compound is the sum of the atomic weights of all atoms in the compound, as represented by its formula. To calculate the formula weight of a compound we must know the correct formula. The formula weight is expressed in atomic mass units. 

Atomic mass Because an atoms mass depends mainly on the number of protons and neutrons it contains, and because protons and neutrons have masses close to 1 amu, you might expect the atomic mass of an element to always be nearly a whole number. However, this is often not the case. The explanation involves how atomic mass is defined. The atomic mass of an element is the weighted average mass of the isotopes of that element. Because isotopes have different mass, the weighted average is not a whole number. The calculation of the atomic mass of chlorine is illustrated in Figure 4.18. 

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