Question

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?

Explanation:

Step1: Calculate the contribution of Gallium - 69

The formula for the contribution of an isotope to the average atomic mass is \( \text{Contribution}=\text{Relative abundance}\times\text{Molar mass} \).
For Gallium - 69, the relative abundance \( x_1 = 60.11\%=0.6011 \) and molar mass \( m_1 = 68.9256\space g/mol \).
The contribution \( C_1=x_1\times m_1=0.6011\times68.9256 \)

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Step2: Calculate the contribution of Gallium - 71

For Gallium - 71, the relative abundance \( x_2=39.89\% = 0.3989 \) and molar mass \( m_2 = 70.9247\space g/mol \)
The contribution \( C_2=x_2\times m_2=0.3989\times70.9247 \)

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Step3: Calculate the average atomic mass

The average atomic mass \( M = C_1 + C_2 \)

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Answer:

The average atomic mass of Gallium is approximately \( 69.72\space g/mol \)