Calculating Masses

* Relative Atomic Mass
* % Abundance of the Lighter Isotope

## Relative Atomic Mass

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100

{\displaystyle {(isotope 1 mass \times Relative Abundance)+(isotope 2 mass \times Relative Abundance) +(isotope 3 mass \times Relative Abundance) \over 100}}

### What Is Relative Atomic Mass

The Relative Atomic Mass is the weight in grams of atoms of an element contained in 12g of carbon-12

### Calculating Relative Atomic Mass

The formula is for Relative Atomic Mass is:

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100

{\displaystyle {(isotope 1 mass \times Relative Abundance)+(isotope 2 mass \times Relative Abundance) +(isotope 3 mass \times Relative Abundance) \over 100}}

The number of isotopes averages on the top by 100 depends on how much isotopes there are, for example:

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100

{\displaystyle {(isotope 1 mass \times Relative Abundance) \over 100}}
 2

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100

{\displaystyle {(isotope 1 mass \times Relative Abundance)+(isotope 2 mass \times Relative Abundance) \over 100}}
 3

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100

{\displaystyle {(isotope 1 mass \times Relative Abundance)+(isotope 2 mass \times Relative Abundance) +(isotope 3 mass \times Relative Abundance) \over 100}}

### Examples

Ag/Silver has 2 Isotopes:

Ag

107

{\displaystyle \ce{^{107}\_Ag
}}

Ag

109

{\displaystyle \ce{^{109}\_Ag}}

 Working Out

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100

{\displaystyle {(isotope 1 mass \times Relative Abundance)+(isotope 2 mass \times Relative Abundance) \over 100}}

(
106.9
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51.8
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48.2
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100

{\displaystyle {(106.9 \times 51.8)+(108.9 \times 48.2) \over 100}}

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5537.42
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5248.98
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100

{\displaystyle {(5537.42)+(5248.98) \over 100}}

10786.4
100

{\displaystyle {10786.4 \over 100}}

 Relative Atomic Mass = 107.864

## Relative Abundance of the Lighter Isotope

### What Is % Abundance of the lighter Isotope?

the percentage of atoms with a specific atomic mass, in this case we are finding the % abundance of the Lighter Isotope

### Examples

6

Li

{\displaystyle \ce{6Li}}

RAM = 6.02

6

Li

{\displaystyle \ce{6Li}}

RAM = 7.02

6

Li

{\displaystyle \ce{6Li}}

RAM = 6.02

6

Li

{\displaystyle \ce{6Li}}

 Abundance of 6:02 Isotope = x
Abundance of 7:02 Isotope = 100-x

# 6.94
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100

{\displaystyle 6.94= (6.02 \times x) + (7.02 \times(100-x)\over 100}

# 694
6.02
x
702
7.02
x

{\displaystyle 694= 6.02 x + 702 + 7.02 x }

694
−
# 702
−
x

{\displaystyle 694 - 702= -x
}

−
# 8
−
x

{\displaystyle -8= -x
}

−
# x
−
8

{\displaystyle -x = -8
}

# x
8

{\displaystyle x=8}

 Abundance of the lighter microscope