I need to find the average molar mass of an unknown element. The atomic mass is 120; the mass numbers of isotopes are 295, 296, 297, 298 and 299; the percent of each isotope is 2.356%, 4.325%, 15.652%, 48.452% and 29.215%. The mass of the neutron is 1.67262164x10^-24g and the mass of a proton is 1.67492721x10^-24g. The mass defect is 0.76132613%.
mass proton x 120 = ?p
mass neutron x (29?-120) = ?n
total mass = ?p+?n x %mass def/100 = ?mass isotope.
(mass isotope x %/100) + (mass isotope x %/100) ........etc for all the isotopes. The total is the average atomic mass.
To find the average molar mass of the unknown element, you will need to calculate the weighted average of the masses of its isotopes, taking into account their relative abundance.
Here are the steps to find the average molar mass:
1. Convert the given percentages of each isotope into decimal form. For example, 2.356% becomes 0.02356, 4.325% becomes 0.04325, and so on.
2. Next, calculate the mass of each isotope by subtracting the mass defect from the atomic mass. The mass defect is given as 0.76132613%, so for an isotope with a mass number of 295, the mass would be (120 - 0.0076132613% / 100) = 119.999992387.
3. Multiply the mass of each isotope by its relative abundance (converted to decimal form) to obtain the contribution of each isotope to the average molar mass.
For example, for the isotope with mass number 295: (119.999992387 g/mol) * 0.02356 = 2.819165179572 g/mol.
4. Repeat this calculation for each isotope, using the given data.
5. Add up all the contributions from step 3 to get the total mass of all the isotopes.
For example, adding the contributions of each isotope: 2.819165179572 + (mass of isotope 296 * abundance of isotope 296) + (mass of isotope 297 * abundance of isotope 297) + (mass of isotope 298 * abundance of isotope 298) + (mass of isotope 299 * abundance of isotope 299) = total mass.
6. Finally, divide the total mass by the sum of the relative abundances (converted to decimal form) to find the average molar mass of the unknown element.
For example, to find the average molar mass: total mass / (0.02356 + 0.04325 + 0.15652 + 0.48452 + 0.29215) = average molar mass in grams/mole.
By following these steps, you should be able to calculate the average molar mass of the unknown element.