Question

1. fill in the following table (provide answers with two digits after the decimal):

the average mass of lithium is 6.941 amu

Explanation:

Step1: Calculate the abundance of \(^{7}\text{Li}\)

The sum of abundances of all isotopes is \(100\%\). Let the abundance of \(^{7}\text{Li}\) be \(x\). Then \(x = 100\% - 7.59\%=92.41\%\)

Step2: Use the formula for average atomic mass

The formula for average atomic mass \(M=\sum_{i}m_{i}a_{i}\), where \(m_{i}\) is the mass of isotope \(i\) and \(a_{i}\) is its abundance (in decimal). Let \(m_1 = 6.015122\) amu, \(a_1=0.0759\), \(m_2\) be the mass of \(^{7}\text{Li}\), \(a_2 = 0.9241\), and \(M = 6.941\) amu.
We substitute into the formula: \(6.941=6.015122\times0.0759 + m_2\times0.9241\)

First, calculate \(6.015122\times0.0759\approx0.4566\)
Then rewrite the equation as \(6.941- 0.4566=m_2\times0.9241\)
\(6.4844=m_2\times0.9241\)
Solve for \(m_2\): \(m_2=\frac{6.4844}{0.9241}\approx7.02\) amu

Answer:

Isotope	Mass	Abundance
\(^{7}\text{Li}\)	\(7.02\) amu	\(92.41\%\)