i need help if i want to have my birthday this year i need to get at least a d- in chem please help

Question

A newly discovered element is given the symbol Z. The element is found to have two dominant isotopes, Z-185 and Z-188. The mass of Z-185 is measured to be 184.825 amu and its percent abundance is 34.41. If the average atomic mass of Z is 187.693, what is the mass (in amu) of Z-188?

Answer 1

Hi Abby! I'd love to help!

When it comes to isotopes and finding the average atomic mass, think of it like a pie chart. The whole circle represents all of the known isotopes for that element, while the pie pieces represent fractions of a specific isotope.

What this means is that for element Z, is its pie chart would have two pie pieces--one for each dominant isotope. One pie piece represents Z-185 and it makes up 34.41% of the 100% total. This means that the other isotope, Z-188 must make up the difference between 100%-34.41% = 65.59%, since only 2 isotopes make up the element.

Now that we have the percent abundances for each of the two isotopes, we can use that information to calculate the relative abundance. We do this by converting each percent into a decimal by dividing by 100.

Z-185 = 34.41%/100 = 0.3441 Z-188 = 65.59%/100 = 0.6559

In order to calculate the weighted average atomic mass for the element (the WAAM!), we need to multiply each isotope's relative abundance by its atomic mass. We add those together to get the WAAM.

WAAM = RA(Z-185)*mass(Z-185) + RA(Z-188)*mass(Z-188)

In the problem, they gave us the WAAM and the mass of Z-185 and are asking us to work backwards from there to solve for the mass of Z-188.

Plugging in our known values,

187.693 amu = 0.3441*184.825 amu + 0.6559*mass(Z-188)

Solving for the mass of Z-188,

187.693 amu = 0.3441*184.825 amu + 0.6559*mass(Z-188)

187.693 amu = 63.598 amu + 0.6559*mass(Z-188)

123.798 amu = 0.6559*mass(Z-188)

mass(Z-188) = 188.745 amu

This means that the mass of the other isotope has to be 188.745 amu. Hope this helps!