Question

question 2: consider the element chlorine (cl) from the periodic table. chlorine has two naturally - occurring isotopes: chlorine - 35: atomic mass = 34.968 amu, abundance = 75.77%; chlorine - 37: atomic mass = 36.966 amu, abundance = 24.23%. part a: calculate the atomic mass of chlorine (cl). show all your calculations clearly. part b: explain why the average atomic mass of an element is often not a whole number. what factors contribute to this and how does the presence of isotopes play a role in this?

Explanation:

Step1: Recall atomic - mass formula

The formula for the average atomic mass ($A_{avg}$) of an element with isotopes is $A_{avg}=\sum_{i} (m_i\times p_i)$, where $m_i$ is the mass of the $i$-th isotope and $p_i$ is its percent - abundance (expressed as a decimal).

Step2: Convert percent - abundances to decimals

For chlorine - 35: $p_1 = 75.77\%=0.7577$, and $m_1 = 34.968$ amu. For chlorine - 37: $p_2=24.23\% = 0.2423$, and $m_2 = 36.966$ amu.

Step3: Calculate the average atomic mass

$A_{avg}=(m_1\times p_1)+(m_2\times p_2)=(34.968\times0.7577)+(36.966\times0.2423)$
$34.968\times0.7577 = 34.968\times(0.75 + 0.0077)=34.968\times0.75+34.968\times0.0077=26.226 + 0.2692536=26.4952536$
$36.966\times0.2423=(37 - 0.034)\times0.2423=37\times0.2423-0.034\times0.2423 = 8.9651-0.0082382 = 8.9568618$
$A_{avg}=26.4952536 + 8.9568618=35.4521154\approx35.45$ amu

Step4: Explain non - whole atomic mass

The average atomic mass of an element is often not a whole number because elements exist as a mixture of isotopes. Each isotope has a different mass and a certain natural abundance. The average atomic mass is a weighted average of the masses of these isotopes based on their abundances.

Answer:

Part A: The average atomic mass of chlorine is approximately 35.45 amu.
Part B: The average atomic mass of an element is not a whole number because elements are composed of a mixture of isotopes with different masses and natural abundances. The average atomic mass is a weighted - average of the masses of these isotopes.