A compound $X$ contains $32\%$ of $A,20\%$ of $B$ and remaining percentage of $C$. Then, the empiric

Question

A compound $X$ contains $32\%$ of $A,20\%$ of $B$ and remaining percentage of $C$. Then, the empirical formula of $X$ is :(Given atomic masses of $A = 64;B = 40;C = 32u$ )

Accepted Answer

Sol. [Key Concept: Empirical formula from mass composition]Take 100 g of compound.The masses of A, B and C are 32, 20 and 48 g.Their mole amounts are 32/64 = 0.5, 20/40 = 0.5 and 48/32 = 1.5.Dividing by 0.5 gives A:B:C = 1:1:3.The empirical formula is ABC₃, option (4). Element Mass percentage % No. of moles No. of moles/ Smallest number Simplest whole number A 32% $$\frac{32}{64} = \frac{1}{2}$$ $$\frac{1}{2} 	imes 2$$ = 1 B 20% $$\frac{20}{40} = \frac{1}{2}$$ $$\frac{1}{2} 	imes 2$$ = 1 C 48% $$\frac{48}{32} = \frac{3}{2}$$ $$\frac{3}{2} 	imes 2$$ = 3

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Element	Mass percentage %	No. of moles	No. of moles/ Smallest number	Simplest whole number
A	32%	$$\frac{32}{64} = \frac{1}{2}$$	$$\frac{1}{2} \times 2$$	= 1
B	20%	$$\frac{20}{40} = \frac{1}{2}$$	$$\frac{1}{2} \times 2$$	= 1
C	48%	$$\frac{48}{32} = \frac{3}{2}$$	$$\frac{3}{2} \times 2$$	= 3