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Define weighted average and average in Chemistry and explain the difference between the two.

Define weighted average and average in Chemistry and explain the difference between the two.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Define weighted average and average in Chemistry and explain the difference between the two.
To find the average atomic mass of neon, we will use the equation above and take the abundance of the first isotope times the mass of the first isotope plus the abundance of the second isotope times the mass of the second isotope plus the abundance of the third isotope times the mass of the third isotope. However, you might recall from your math courses that when you use a percentage in a calculation you always want to use the decimal form, meaning you must first divide the percentage by 100. The equation would then look like: = (0.9048 x 19.9924 amu) + (0.0027 x 20.9938 amu) + (0.0925 x 21.9914 amu) 0.0516 amu 2.034 amu = 18.089 amu = 20.18 amu + +
Transcribed Image Text:To find the average atomic mass of neon, we will use the equation above and take the abundance of the first isotope times the mass of the first isotope plus the abundance of the second isotope times the mass of the second isotope plus the abundance of the third isotope times the mass of the third isotope. However, you might recall from your math courses that when you use a percentage in a calculation you always want to use the decimal form, meaning you must first divide the percentage by 100. The equation would then look like: = (0.9048 x 19.9924 amu) + (0.0027 x 20.9938 amu) + (0.0925 x 21.9914 amu) 0.0516 amu 2.034 amu = 18.089 amu = 20.18 amu + +
Since the abundances are not equal, we cannot do a typical simple average where we just add them u and divide by two. Instead, we need to perform a weighted average. The formula to calculate the average atomic mass is: average atomic mass=(relative abundance x mass of isotope) Remember that is the symbol for sum. In other words, we will take the sum of the relative abundance of each isotope multiplied by its mass. Example Neon has three naturally occurring isotopes. Symbol Ne-20 Ne-21 Ne-22 Mass Isotopic mass Percent natural number (amu) 20 21 22 19.9924 20.9938 21.9914 abundance 90.48% 0.27% ...
Transcribed Image Text:Since the abundances are not equal, we cannot do a typical simple average where we just add them u and divide by two. Instead, we need to perform a weighted average. The formula to calculate the average atomic mass is: average atomic mass=(relative abundance x mass of isotope) Remember that is the symbol for sum. In other words, we will take the sum of the relative abundance of each isotope multiplied by its mass. Example Neon has three naturally occurring isotopes. Symbol Ne-20 Ne-21 Ne-22 Mass Isotopic mass Percent natural number (amu) 20 21 22 19.9924 20.9938 21.9914 abundance 90.48% 0.27% ...
Expert Solution
Step 1 Average

Average is a summation of quantities, divided by the total quantities, to get a single number.

For example:

In a gas cylinder 3 gases are present. Average mass in cylinder will be equal to

 Mass of O2 gas=10gMass of N2 gas=20gMass of He gas=30gAverage mass of gases in cylinder=?

 

Average=Mass of O2+Mass of N2+Mass of HeNumber of gases in cylinderAverage=10g+20g+30g3=20g

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