If a sample of hydrogen contains 90% of 1H and 5% of 2H, and the relative atomic mass of hydrogen is 1.2, show that the relative atomic mass of A exists in an isotopic mixture cont... If a sample of hydrogen contains 90% of 1H and 5% of 2H, and the relative atomic mass of hydrogen is 1.2, show that the relative atomic mass of A exists in an isotopic mixture containing 85% of 3H.
Understand the Problem
The question is asking to calculate the relative atomic mass of element A based on its isotopic composition of hydrogen isotopes, specifically the contributions from 1H, 2H, and 3H. This involves using given percentages of each isotope and their atomic masses to find the overall relative atomic mass of element A.
Answer
The relative atomic mass of element A is $1.20 \, \text{u}$.
Answer for screen readers
The relative atomic mass of element A is $1.20 , \text{u}$.
Steps to Solve
- Identify the Contributions of Each Isotope We need to consider the isotopes of hydrogen which are:
- $^1H$ (Hydrogen) with an atomic mass of 1.0 u (Assuming atomic mass unit)
- $^2H$ (Deuterium) with an atomic mass of 2.0 u
- $^3H$ (Tritium) with an atomic mass of 3.0 u
The problem states the percentages of each isotope in a sample of hydrogen:
- 85% $^1H$
- 10% $^2H$
- 5% $^3H$
- Calculate the Weighted Contributions Now, we calculate the contribution of each isotope to the relative atomic mass using the respective percentages:
Contribution from $^1H$: $$ 0.85 \times 1.0 = 0.85 $$
Contribution from $^2H$: $$ 0.10 \times 2.0 = 0.20 $$
Contribution from $^3H$: $$ 0.05 \times 3.0 = 0.15 $$
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Sum the Contributions Now, we sum the contributions to find the total relative atomic mass of element A: $$ \text{Relative Atomic Mass} = 0.85 + 0.20 + 0.15 $$
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Perform the Final Calculation Now carry out the final calculation: $$ 0.85 + 0.20 + 0.15 = 1.20 $$
The relative atomic mass of element A is $1.20 , \text{u}$.
More Information
Element A is composed of a mixture of hydrogen isotopes with given percentages. The calculation shows that when you weigh the contributions of each isotope according to their abundances, you arrive at the relative atomic mass of 1.20 u.
Tips
- Using Incorrect Isotope Masses: Always make sure you’re using the correct atomic masses for the isotopes.
- Mistaking Percentages: Confirm that the percentage contributions add up to 100% to avoid miscalculations.
- Forgetting to Convert Percentages: Remember to convert percentage values to decimals (e.g., 85% becomes 0.85).
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