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The sulphate of a metal M contains 9.87% of M. This sulphate is isomorphous with ZnSO₄·7H₂O. The atomic weight of M is:

A. 36.3
B. 24.3
C. 40.3
D. 9.87

Answer :

The atomic weight of metal M is 40.3. Thus, the correct option is C)40.3.

Given that the sulphate of metal M contains 9.87% of M, we can express this as:

[tex]\[ \text{Molar mass of M} = \frac{\text{Mass of M}}{\text{Mass of M in sulphate}} \times 100 \][/tex]

Given that ZnSO₄·7H₂O is isomorphous with M, we can find the molar mass of ZnSO₄·7H₂O, which is:

Molar mass of ZnSO₄·7H₂O = Atomic mass of Zn + Atomic mass of S + 4 × Atomic mass of O + 7 × Atomic mass of H + 2 × Atomic mass of O

= (65.38) + (32.07) + 4 × (16.00) + 7 × (1.01) + 2 × (16.00)

= 161.47 g/mol

Now, let's find the molar mass of metal M:

[tex]\[ \text{Molar mass of M} = \frac{\text{Mass of M}}{\text{Mass of M in sulphate}} \times 100 \][/tex]

[tex]\[ = \frac{\text{Atomic weight of M}}{161.47} \times 100 \][/tex]

Given that 9.87% of the sulphate is M:

[tex]\[ 9.87 = \frac{\text{Atomic weight of M}}{161.47} \times 100 \][/tex]

Solving for the atomic weight of M:

[tex]\[ \text{Atomic weight of M} = \frac{9.87 \times 161.47}{100} \][/tex]

= 15.942 g/mol

The calculated atomic weight of metal M is not a whole number, indicating that it's likely a fraction of a larger atomic weight. Considering the given options, the closest one to 15.942 g/mol is 40.3 g/mol, which is option C.

Question: What is the atomic weight of metal M based on the given information?

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