Question

How many moles of O2 will be liberated by one
mole of CrO5 in the following reaction?
CrO₅ + H₂SO₄ → Cr₂(SO₄)₃ + H₂O + O₂

Answer 1

CrO₅ + H₂SO₄ → Cr₂(SO₄)₃ + H₂O + O₂ is the given reaction.
if we balance the reaction it would be
4(CrO₅) + 6(H₂SO₄) → 2(Cr₂(SO₄)₃ )+ 6(H₂O) + 7C
therefore 7 moles of  O₂ will be liberated

Answer 2

This is an authentic method, {it was confirmed that c_1 = 1}

Balance the chemical equation:

CrO5 + H_2SO_4 --> Cr_2(SO_4)_3 + H_2O + O_2

Add coefficients to all the molecules:

c_1 CrO5 + c_2 H_2SO_4 --> c_3 Cr_2(SO_4)_3 + c_4 H_2O + c_5 O_2

The number of Cr, O, H, and S atoms on both sides of the reaction must be equal:

Cr: | c_1 = 2 c_3

O: | 5 c_1+4 c_2 = 12 c_3+c_4+2 c_5

H: | 2 c_2 = 2 c_4

S: | c_2 = 3 c_3

Since the coefficients are only determined up to a multiplicative constant, set c_3 = 1 and solve for thecoefficients:

c_1 = 2c_2 = 3c_3 = 1c_4 = 3c_5 = 7/2

Since one of the coefficients is a fraction, set c_3 = 2 and repeat the step above to obtain integer coefficients:

c_1 = 4c_2 = 6c_3 = 2c_4 = 6c_5 = 7

Since the coefficients are all integers with a greatest common denominator = 1, 

Substitute the coefficients into the chemical reaction to obtain the balanced equation:4

CrO5 + 6 H_2SO_4 --> 2 Cr_2(SO_4)_3 + 6 H_2O + 7 O_2

Now the number of moles of O2 obtained is 7