Re has two natural occuring isotopes 185 Re and 187 Re with an average atomic mass of 186.207 amu. Re is 62.60% 187Re and the atomic mass of 187Re is 186.956 amu. What is the mass of 185 Re
(0.6260*186.956) + (1-0.6260)*x = 186.207
Solve for x.
Note: if 63.60% is one isotope, the other must be 100-62.60 = ? That's what I used above but changed to fractions instead of percent.
To find the mass of 185 Re, we can use the information given about the average atomic mass and the percentage abundance of 187 Re.
Let's assume the mass of 185 Re is "x" amu.
Given:
- Average atomic mass of Re = 186.207 amu
- Percentage abundance of 187 Re = 62.60%
We also know the atomic mass of 187 Re is 186.956 amu.
The average atomic mass is calculated by taking the weighted average of the isotopes:
Average atomic mass = (mass of isotope 1 * abundance of isotope 1) + (mass of isotope 2 * abundance of isotope 2)
Substituting the values for Re:
186.207 amu = (x amu * abundance of 185 Re) + (186.956 amu * abundance of 187 Re)
Since the percentage abundance of 187 Re is given, we can express it as a decimal by dividing by 100:
62.60% = 0.6260
186.207 amu = (x amu * abundance of 185 Re) + (186.956 amu * 0.6260)
Now let's solve for x:
186.207 amu = (x amu * (1 - 0.6260)) + (186.956 amu * 0.6260)
186.207 amu = (x amu * 0.3740) + (186.956 amu * 0.6260)
186.207 amu = 0.3740x amu + 116.986906 amu
0.3740x amu = 186.207 amu - 116.986906 amu
0.3740x amu = 69.220094 amu
Now, divide both sides of the equation by 0.3740 to isolate x:
x amu = 69.220094 amu / 0.3740
x amu = 185.4300786 amu
Therefore, the mass of 185 Re is approximately 185.43 amu.