Question

Sphalerite shows limited isomorphism. Consider a colorless sphalerite having 33% S and 67% Zn. Then, in a black-coloured sphalerite, with a 15% Fe substitution, the ratio of atomic proportions of Zn to that of Fe is ...........

Hint:

To find the atomic ratio of two elements, calculate the number of moles of each element using the atomic weights and then divide the moles of one element by the moles of the other element.

Answer 1

Correct Answer: 1.1

Given: 
- Atomic weight of Zn = 65.37 
- Atomic weight of Fe = 55.85 
- Atomic weight of S = 32.06 
Step 1: We are given that 15% of Fe is substituted in the sphalerite. Thus, the percentage of Zn is 85% (since \(100\% - 15\% = 85\%\)).

Step 2: Now, to calculate the ratio of atomic proportions of Zn to Fe, we first calculate the number of moles of Zn and Fe in the given proportions. The formula to calculate the number of moles is: 
\[ \text{Moles} = \frac{\text{Weight percentage}}{\text{Atomic weight}} \]
- Moles of Zn:
\[ \text{Moles of Zn} = \frac{85}{65.37} = 1.3 \]
- Moles of Fe:
\[ \text{Moles of Fe} = \frac{15}{55.85} = 0.27 \]

Step 3: The ratio of Zn to Fe in terms of atomic proportions is:
\[ \text{Ratio of Zn to Fe} = \frac{\text{Moles of Zn}}{\text{Moles of Fe}} = \frac{1.3}{0.27} \approx 1.1 \]
Thus, the ratio of atomic proportions of Zn to that of Fe is 1.1. 
\[ \boxed{1.1} \]