Question

The molality of a 1L solution with x% H2SO4 is 9. The weight of solvent is 910 grams. The value of x is?
A: 90
B: 80.3
C: 30.38
D: 46.87
THE ANSWER IS (D)..... PLEASE GIVE DETAILED SOLUTION

Answer 1

The molality of a solution is 9 when there are 9 moles by kg of solvent . For 910g =0.91kg there are 0.91*9= 8.19 moles of H2SO4 by kg of water . The molar weight of H2SO4=2*1+32+4*16=98g and so you have 98*8.19=802.62g =0.80262 of H2SO4 for 1 kg of water 
the proportion in weight of H2SO4 is p= 0.80262/1+0.80262=0.445 

so if you have a solution, with a density of 1g/cc, this corresponds to1000g in a liter or 1kg 

x=445/1000=0.445=44.5%   which is equalvalent to 46.87%