If ca is the new standard of atomic mass and is assigned a value of 50.00 amu, what is the molar mass of aluminium acetate using this standard?

how does one solve this?

848.1 g/mol

Explanation:

Data given:

Standard of atomic mass of Ca = 50 amu

molar mass of Aluminium Acetate = ?

Solution:

Relative atomic mass represented by Ar. It is ratio of actual mass with respect to the 1/12th mass of C-12 but here Ca-50 is standard.

Formula of  Aluminium Acetate = Al(CH₃COO)₃

In order to calculate Ar

first we will calculate 1/50 of Ca

As we know

         mass of 1/12 of C-12 = 1.993 x 10⁻²⁶/12 = 1.661 x 10⁻²⁷ Kg

So, for Ca-50

        mass of 1/50 of Ca-50 = 1.993 x 10⁻²⁶/50 = 3.986 x 10⁻²⁸ Kg

Now

 Relative Atomic mass for element X = rest mass of "X"/ 3.986 x 10⁻²⁸ Kg . . . . . . (1)

First we have to know the relative atomic masses of Aluminium, carbon, hydrogen, oxygen atoms involve in Aluminium Acetate formula with respect to new standard Ca-50

By using equation-1 we can calculate Ar for which we have reported rest masses of atoms as below

Rest mass of Aluminium = 4.48 x 10⁻²⁶ Kg

Rest mass of carbon = 1.993 x 10⁻²⁶ Kg

Rest mass of hydrogen = 1.608 x 10⁻²⁷ Kg

Rest mass of oxygen = 2.657x10⁻²⁶ Kg

Now put values in equation 1 for each atom

                     Ar for Aluminium = 112.5  amu

                     Ar for Carbon= 50 amu

                     Ar for hydrogen = 4  amu

                     Ar for Oxygen = 66.6  amu

Now find the molar mass of Al(CH₃COO)₃

molar mass of Aluminium Acetate = Al(CH₃COO)₃

Al(CH₃COO)₃ = 112.5 + 3 (50 + 3(4) + 50 + 66.6 +66.6)

Al(CH₃COO)₃ = 112.5 + 3 (50 + 12 + 50 + 66.6 +66.6)

Al(CH₃COO)₃ = 112.5 + 3 (245.2)

Al(CH₃COO)₃ = 112.5 + 735.6

Al(CH₃COO)₃ = 848.1 g/mol

molar mass of Aluminium Acetate = 848.1 g/mol