We are going to work out the concentration (and from that mol and mass) of the ammonia solution from the know volume and concentration of HCL.
So n(HCl)=0.11*0.2462=0.0027082mol
We know that this reacts with NH3 in a 1:1 ratio
So the mol of NH3 reacted is nreacted(NH3)=n(HCL)=0.0027082 mol
This is the amount in the 20ml that you took (i.e. the alliquot) since this is the amount reacting with the HCL. So the amount in the 250ml solution should be in proportion as these two are the same concentration (since we are just taking it out of one and putting it in the other, no diluting here).
So the amount in the 250ml volumetric flask is 250/20*0.0027082=0.0338525mol.
The original amount has been diluted to get this. So the amount in the original is the same, but the concentration is different (Volume has changed, amount in mol hasn't. Thus the amount in the original is 0.0338525mol.
Now we can work out the original mass of the ammonia in the original solution. so moriginal(NH3)=0.0338525*17=0.5754925g
The original sample (not ammoina, it is the sample i.e. ammonia mixed in other stuff, water, impurities, other ingredients) has mass 9.97g.
So the percentage by mass of ammonia will be 0.5754925/9.97*100=5.77% (w/w)
So basically the steps here are:
1. Determine the amount of mole of the known solution (the HCL)
2. From this work out the amount of the unknown solution reacted (using mol ratios)
3. Next work out how much the original sample will have by using ratios of volume originally over volume taken out
4. Find mass of original (NH3)
5. Divide mass of (NH3) by total mass of the original sample *100
6. Bingo.