Question

average atomic mass & percent abundance problems
name
date
per
average atomic mass
copper
\\( \begin{array} { l l l l l l l } { _ { 2 9 } ^ { 6 3 } mathrm { cu } } & { 6 9. 0 9 % } & { 6 2. 9 2 9 8 } & { ________ } & { } } & { + = } & { ________ } \\\\ { _ { 2 9 } ^ { 6 5 } mathrm { cu } } & { 3 0. 9 1 % } & { 6 4. 9 2 7 8 } & { ________ } & { } & { } & { } end{array} \\)
magnesium
\\( \begin{array} { l l l l l l l } { _ { 1 2 } ^ { 2 4 } mathrm { mg } } & { 7 8. 7 0 % } & { 2 3. 9 8 5 } & { ________ } & { } & { } & { } \\\\ { _ { 1 2 } ^ { 2 5 } mathrm { mg } } & { 1 0. 1 3 % } & { 2 4. 9 8 5 8 } & { ________ } & { } } & { + = } & { ________ } \\\\ { _ { 1 2 } ^ { 2 6 } mathrm { mg } } & { 1 1. 1 7 % } & { 2 5. 9 8 2 6 } & { ________ } & { } & { } & { } end{array} \\)
the element gallium has two stable isotopes, gallium - 69 and gallium - 71. gallium - 69 has a molar mass of 68.9256 g/mol and gallium - 71 has a molar mass of 70.9247 g/mol. gallium - 69 has a relative abundance of 60.11% and gallium - 71 has a relative abundance of 39.89%. what is the average atomic mass of gallium?
thallium has two stable isotopes, thallium - 203 and thallium - 205. thallium - 203 has a molar mass of 202.9723 g/mol and a relative abundance of 29.52%. thallium - 205 has a molar mass of 204.9744 g/mol and a relative abundance of 70.48%. what is the average atomic mass of thallium?
three isotopes of argon occur in nature - \\( _ { 1 8 } ^ { 3 6 } mathrm { ar }, _ { 1 8 } ^ { 3 8 } mathrm { ar } \\), and \\( _ { 1 8 } ^ { 4 0 } mathrm { ar } \\)
calculate the average atomic mass of argon to two decimal places, given the following relative atomic masses and abundances of each of the isotopes; argon - 36 (35.97 amu, 0.337%) argon - 38 (37.96 amu; 0.063%) and argon - 40 (39.96 amu; 99.600%)

Explanation:

Step1: <Formula for average atomic mass>

The formula for average atomic mass \(M_{avg}=\sum_{i}(M_i\times A_i)\), where \(M_i\) is the mass of isotope \(i\) and \(A_i\) is the abundance of isotope \(i\) (in decimal form).

Step2: <For Gallium>

For Gallium - 69: \(M_1 = 68.9256\space g/mol\), \(A_1=0.6011\)
For Gallium - 71: \(M_2 = 70.9247\space g/mol\), \(A_2 = 0.3989\)
\(M_{avg(Ga)}=(68.9256\times0.6011)+(70.9247\times0.3989)\)

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Step3: <For Thallium>

For Thallium - 203: \(M_1 = 202.9723\space g/mol\), \(A_1=0.2952\)
For Thallium - 205: \(M_2 = 204.9744\space g/mol\), \(A_2 = 0.7048\)
\(M_{avg(Tl)}=(202.9723\times0.2952)+(204.9744\times0.7048)\)

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Step4: <For Argon>

For Argon - 36: \(M_1 = 35.97\space amu\), \(A_1 = 0.00337\)
For Argon - 38: \(M_2 = 37.96\space amu\), \(A_2=0.00063\)
For Argon - 40: \(M_3 = 39.96\space amu\), \(A_3 = 0.996\)
\(M_{avg(Ar)}=(35.97\times0.00337)+(37.96\times0.00063)+(39.96\times0.996)\)

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Answer:

• The average atomic mass of Gallium is \(69.72\space g/mol\)
• The average atomic mass of Thallium is \(204.38\space g/mol\)
• The average atomic mass of Argon is \(39.95\space amu\)