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Chapter 3: Problem 41

The element rhenium (Re) has two naturally occurring isotopes, \(^{185}\) \(\mathrm{Re}\) and \(^{187}\) \(\mathrm{Re},\) with an average atomic mass of 186.207 u. Rhenium is 62.60\(\%\) of Re, and the atomic mass of \(^{187}\)Re is 186.956 u. Calculate the mass of \(^{185}\)Re.

Short Answer

Expert verified
The mass of isotope \(^{185}Re\) is approximately 185.459 u.

Step by step solution

01

Find the fraction of \(^{185}Re\)

Since we have the relative abundance of \(^{187}Re\), we can find the fraction of \(^{185}Re\) as follows: Fraction of \(^{185}Re\) = 1 - Fraction of \(^{187}Re\) Fraction of \(^{185}Re\) = 1 - 0.6260 Fraction of \(^{185}Re\) = 0.3740
02

Set up the equation for average atomic mass

Using the given average atomic mass and the formula mentioned above, we get: 186.207 u = (0.3740 × mass of \(^{185}Re\)) + (0.6260 × 186.956 u)
03

Solve for the mass of \(^{185}Re\)

Now, we need to solve for the mass of \(^{185}Re\): 186.207 u = (0.3740 × mass of \(^{185}Re\)) + (0.6260 × 186.956 u) To isolate the term with mass of \(^{185}Re\), subtract the term with the mass of \(^{187}Re\): mass of \(^{185}Re\) × 0.3740 = 186.207 u - (0.6260 × 186.956 u) Now, divide by 0.3740 to get the mass of \(^{185}Re\): mass of \(^{185}Re\) = (186.207 u - (0.6260 × 186.956 u)) / 0.3740 mass of \(^{185}Re\) ≈ 185.459 u So, the mass of isotope \(^{185}Re\) is approximately 185.459 u.

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