In a crystalline solid, atoms of element P form a ccp lattice. Atoms of element Q occupy 1 3 of the tetrahedral voids and atoms of element R occupy 1 2 of the octahedral voids. If the molar masses of P, Q, and R are 20 g mol ⁻¹ , 40 g mol ⁻¹ , and 40 g mol ⁻¹ respectively, the mass percentage of P in the compound is _______. (Nearest integer)

Step-by-step solution

Let the number of atoms of element P in the ccp lattice be N . The number of tetrahedral voids is 2N and the number of octahedral voids is N . Number of Q atoms = 1 3 2N = 2N 3 Number of R atoms = 1 2 N = N 2 The ratio of the number of atoms of P, Q, and R is: P : Q : R = N : 2N 3 : N 2 = 1 : 2 3 : 1 2 Multiplying by 6 to get whole numbers, the ratio is 6 : 4 : 3 . The empirical formula of the compound is P₆Q₄R₃ . Molar mass of the empirical formula = (6 20) + (4 40) + (3 40) = 120 + 160 + 120 = 400 g mol ⁻¹ Mass p