UPSC Civil Services (Mains), Chemistry optional · 2018 · Paper I
Q2(d)(ii). Number of K⁺ and Cl⁻ ions in 1.00 g of KCl
Question
The potassium chloride crystal structure is like that of sodium chloride. The unit cell contains four potassium ions and four chloride ions. Given that the size of unit cell as 6.29 Å and the density of potassium chloride as 1.99 g/c.c. Calculate the number of potassium ions and chloride ions in 1.00 g of the salt.
Answer in brief
1.00 g of KCl contains 8.08×10²¹ K⁺ ions and 8.08×10²¹ Cl⁻ ions.
Key points
- a=6.29 Å=6.29×10⁻⁸ cm; a³=2.489×10⁻²²cm³
- Mass of one unit cell =ρ a³=1.99×2.489×10⁻²²=4.952×10⁻²² g
- Number of unit cells in 1.00 g =1.004.952×10⁻²²=2.019×10²¹
- 4×2.019×10²¹ N(K⁺)=N(Cl⁻)=8.08×10²¹
The full model answer
Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.
- a=6.29 Å=6.29×10⁻⁸ cm; a³=2.489×10⁻²²cm³
- Mass of one unit cell =ρ a³=1.99×2.489×10⁻²²=4.952×10⁻²² g
- Number of unit cells in 1.00 g =1.004.952×10⁻²²=2.019×10²¹
- Each cell holds 4 K⁺ and 4 Cl⁻: 4×2.019×10²¹ N(K⁺)=N(Cl⁻)=8.08×10²¹
- Check: 1.00/74.55 mol ×6.022×10²³=8.08×10²¹ formula units. The data are consistent; the density calculated from a is 4M/N_Aa³=1.990 g cm⁻³.
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All parts of Question 2
- 2(a)(i) Orbital and probability density5 marks
- 2(a)(ii) Radial, angular and total nodes5 marks
- 2(a)(iii) If Planck's constant were zero5 marks
- 2(b)(i) Significance of the Kelvin equation5 marks
- 2(b)(ii) Effect of temperature on viscosity5 marks
- 2(c) Bond orders of H₂⁺, Ne₂, CN⁻, NO and HF; order of stability15 marks
- 2(d)(i) Derivation of Bragg's equation5 marks
- 2(d)(ii) Number of K⁺ and Cl⁻ ions in 1.00 g of KCl5 marks