The atomic weight of copper is 63.546 amu. the two naturally occuring isotopes of copper have the following masses 63cu, 62.9298 amu, 65cu, 64.9278 amu. calculate percent of 63cu in naturally occuring copper

The percent isotopic abundance of Cu-65 is 30.79 %.

The percent isotopic abundance of Cu-63 is 69.21 %.

Explanation:

we know there are two naturally occurring isotopes of carbon, Cu-63 (62.9298 amu)  and Cu-65 (64.9278 amu)

First of all we will set the fraction for both isotopes

X for the isotopes having mass 62.9298 amu

1-x for isotopes having mass 64.9278 amu

The average atomic mass of copper is 63.546 amu.

we will use the following equation,

62.9298 x + 64.9278 (1-x) = 63.546

62.9298x +  64.9278 -  64.9278x = 63.546

62.9298x - 64.9278x = 63.546  - 64.9278

-1.998 x = -1.3828

x=-1.3828 / -1.998

x= 0.6921

0.6921 × 100 = 69.21 %

69.21 % is abundance of Cu-63 because we solve the fraction x.

now we will calculate the abundance of Cu-65.

(1-x)

1-0.6921 = 0.3079

0.3079 × 100 = 30.79 %

30.79 % for Cu-65.

1. for the first question, we must find the mass of the anhydrous salt, mgso₄. the molar mass for mgso₄·7h₂o is 246.47 g/mol, while that of mgso₄ is 120.37 g/mol.7.834 g mgso₄·7h₂o * 1 mol mgso₄·7h₂o/246.47 g * 1 mol mgso₄/1 mol mgso₄·7h₂o * 20.37 g mgso₄/mol = 0.647 g mgso₄

2. mass of water = mass of sample - mass of anhydrous salemass of water = 7.834 - 0.647 = 7.19 gpercent water in hydrate = 7.19/7.834 * 100 = 91.74%