Question

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

Short answer

The mass of${}^{185}\mathrm{Re}$is 184.953 amu.

Step-by-step solution

Definition of Atomic number

Atoms of the same element that have the same count of protons but a different count of neutrons are called isotopes. The atomic number of an element equals its number of protons.

Explanation of percent composition

% of abundance ­of ${}^{185}\mathrm{Re}$+% of abundance of ${}^{187}\mathrm{Re}$equals 100.

So,

% of abundance of${}^{185}\mathrm{Re}$+62.60=100

% of abundance of ${}^{185}\mathrm{Re}$=100-62.60

% of abundance of ${}^{185}\mathrm{Re}$=37.40%

The mass of  Re185

$$\begin{gathered} \mathrm{Average}\mathrm{atomic}\mathrm{mass}\mathrm{of}\mathrm{Re}=\left(37.40\%\right)\left(\mathrm{mass}\right)+\left(62.60\%\right)\left(186.956\right) \\ 186.207=\left(\frac{37.40}{100}\right)\left(\mathrm{mass}\right)+\left(\frac{62.60}{100}\right)\left(186.956\right) \\ \mathrm{Atomic}\mathrm{mass}\mathrm{of}{}^{185}\mathrm{Re}=\left(186.207-117.0344\right)\left(\frac{100}{37.40}\right) \\ \mathrm{Atomic}\mathrm{mass}\mathrm{of}{}^{185}\mathrm{Re}=\left(69.1726\right)\left(\frac{100}{37.40}\right) \\ \mathrm{Hence}, \\ \mathrm{Atomic}\mathrm{mass}\mathrm{of}{}^{185}\mathrm{Re}=184.953 \end{gathered}$$