Q.25E - Chemistry (OpenStax)

Question

The average atomic masses of some elements may vary, depending upon the sources of their ores. Naturally occurring, the boron consists of two isotopes with accurately known masses ( ¹⁰B, 10.0129 amu and ¹¹B, 11.0931 amu). The actual atomic mass of boron can vary from 10.807 to 10.819, depending on whether the mineral source is from Turkey or the United States. Calculate the percent abundance leading to the two values of the average atomic masses of boron from these two countries.

Step-by-Step Solution

Answer

From Turkey source: % of ¹⁰B = 26.5% and % 0f ¹¹B = 73.5%

From United States (US) source: % of ¹⁰B = 25.37% and % of ¹¹B = 74.63%

Step 1 – Determine the percentage abundance of Boron from Turkey Source

From Turkey source

Let the percentage abundance of ¹⁰B be X and ¹¹B be 100-X. 

B avg. mass = [(X)×10.0129amu] +[(100-X) × 11.0931amu)]/ 100

10.807 amu = [10.0129X + 1109.31 - 11.0931X]/ 100

1080.7 amu = 1109.31 – 1.0802X

X = (1109.31-1080.7)/ 1.0802 = 26.5%

So, 100-X= 100-26.5= 73.5%

Step 2 – Determine the percentage abundance of Boron from US Source

From US source

Let the percentage abundance of ¹⁰B be X and ¹¹B be 100-X. 

B avg. mass = [(X)×10.0129amu] +[(100-X) × 11.0931amu)]/ 100

10.819 amu = [10.0129X + 1109.31 - 11.0931X]/ 100

1081.9 amu = 1109.31 – 1.0802X

X = (1109.31-1081.9)/ 1.0802 = 25.37%

So, 100-X = 100- 25.37 = 74.63%