The element rhenium (Re) has two naturally occurring isotopes, 185Re and 187Re, with an average atomic mass of 186.207 amu. Rhenium is 62.60% 187Re, and the atomic mass of 187Re is 186.956 amu. Calculate the mass of 185Re. (Give your answer to 3 decimal places.)
To calculate the mass of 185Re, we can use the average atomic mass and the percentages of the two isotopes (185Re and 187Re).
Let's denote the mass of 185Re as x amu.
We know that the average atomic mass is 186.207 amu. This can be expressed as:
(0.6259 * 187Re mass) + (0.3741 * 185Re mass) = 186.207 amu
Substituting in the given masses for 187Re (186.956 amu) and the unknown mass for 185Re (x amu), we have:
(0.6259 * 186.956 amu) + (0.3741 * x amu) = 186.207 amu
Now we can solve for x by rearranging the equation:
(0.3741 * x amu) = 186.207 amu - (0.6259 * 186.956 amu)
Dividing both sides of the equation by 0.3741, we get:
x amu = (186.207 amu - (0.6259 * 186.956 amu)) / 0.3741
Calculating this expression gives us:
x amu ≈ 184.999 amu
Therefore, the mass of 185Re is approximately 184.999 amu (rounded to 3 decimal places).