A complex solid matrix contains elements P, Q, and R. Atoms of P form a Cubic Close Packed (CCP) lat — Solid State Chemistry Question
Question
A complex solid matrix contains elements P, Q, and R. Atoms of P form a Cubic Close Packed (CCP) lattice. Atoms of Q occupy exactly $\frac{1}{3}$ rd of the available tetrahedral voids. Atoms of R perfectly occupy exactly $\frac{1}{2}$ of the available octahedral voids. If the empirical formula is deduced as $P_xQ_yR_z$, what is the minimum integer value for the sum $(x+y+z)$?
Answer: 13
💡 Solution & Explanation
P forms CCP, so $Z=4$. There are 8 TVs; Q occupies $\frac{1}{3} \times 8 = \frac{8}{3}$. There are 4 OVs; R occupies $\frac{1}{2} \times 4 = 2$. The stoichiometric ratio P : Q : R is $4 : \frac{8}{3} : 2$. Multiplying by 3 gives $12 : 8 : 6$, and simplifying yields $6 : 4 : 3$. Thus, the empirical formula is $P_6Q_4R_3$. The sum $x+y+z = 6+4+3=13$.
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