Question

A chromium-containing compound has the formula Cu_xCr_yO₄   and is 35.65% oxygen by mass. Solve for X and Y.

Answer 1

lets take 100 g of this compound

then , there will be 35.65 g of oxygen

and the sum of mass of Cu and Cr will be (100g - 35.65g) = 64.35 g

and lets assume that there are "P" g of Cu

So .. the mass of Cr is ( 100g - 35.65g - P ) = 64.35 - P g

now.... lets divide the the mass of each by its molar mass and get the amount of mole

Oxygen = 35.65/16 mol = 2.22 mol

Cu = P/63.5 mol

Cr = (64.35 - P) / 51.9 mol

now the ratio of  moles of O : Fe : Cr = 4 : X : Y

and we know that the  there are 2.22 moles of O and it should be divide by 0.555 in order to get 4.

so lets divide the no.of moles of each by 0.555

O : Cu : Cr = 2.22/0.555 : P/(63.5*0.555) : (64.35 - P)/(51.9*0.555)


but here 0.555 should equal to the lowest no.of moles .. means

either P/63.5 = 0.555 or (64.35 - P )/ 51.9 equals to 0.555

if P/63.5 = 0.555

then P =  35.24

so... Cr mass will be 29.11 g

then O : Cu : Cr = 35.65/16 : 35.24/63.5 : 29.11/51.9

divide them by 0.555

   O : Cu : Cr = 4 : 0.999 : 1.01
on rounding off;
O : Cu : Cr = 4 : 1 : 1

So, X = 1 and Y = 1