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Chapter 2: Problem 36

Rubidium has two naturally occurring isotopes, rubidium-85 (atomic mass \(=84.9118\) amu; abundance \(=72.15 \%\) ) and rubidium-87 (atomic mass = 86.9092 amu; abundance = 27.85\(\%\) ). Calculate the atomic weight of rubidium.

Short Answer

Expert verified
The atomic weight of rubidium is approximately 85.47 amu, calculated using the formula: Atomic weight = (Atomic mass of Rubidium-85 × Decimal abundance of Rubidium-85) + (Atomic mass of Rubidium-87 × Decimal abundance of Rubidium-87).

Step by step solution

01

Understand the Formula for Atomic Weight

To calculate the atomic weight of an element with multiple isotopes, use the following formula: Atomic weight = (Atomic mass of isotope 1 × Abundance of isotope 1) + (Atomic mass of isotope 2 × Abundance of isotope 2) + ... Notice that the abundances should be in decimal form for this calculation, so we'll have to convert the given percentage values into decimals.
02

Convert Percent Abundances to Decimal Abundances

To convert the given percent abundances into decimal abundances, simply divide the percentages by 100. Decimal abundance of Rubidium-85: \( \frac{72.15}{100} = 0.7215 \) Decimal abundance of Rubidium-87: \( \frac{27.85}{100} = 0.2785 \)
03

Calculate the Atomic Weight of Rubidium Using the Formula

Now that we have the decimal abundances, plug the given values into the formula for atomic weight: Atomic weight = (Atomic mass of Rubidium-85 × Decimal abundance of Rubidium-85) + (Atomic mass of Rubidium-87 × Decimal abundance of Rubidium-87) Atomic weight = (84.9118 amu × 0.7215) + (86.9092 amu × 0.2785)
04

Perform the Calculations

Calculate the individual parts of the formula and then sum them up to find the atomic weight of rubidium: Atomic weight = (84.9118 amu × 0.7215) + (86.9092 amu × 0.2785) = 61.26002 amu + 24.209714 amu Atomic weight = 85.469734 amu
05

Write Down the Answer

The atomic weight of rubidium is approximately 85.47 amu (rounded to two decimal places).

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