Help with this simple volumetric question!

[sanam]

Hi guys this is a simple question and i dont have the solution to it and im getting kinda stuck so if anyone could answer this, thanks in advance!

To analyze the ammonia content of a brand of cloudy ammonia, a student performed the following procedure:
-10.213g of cloudy ammonia was weighed out and immediately made up to 250 ml in a volumetric flask.
-A 20.00ml aliquot was then taken and immediately reacted with 20.00ml of 0.105M hydrochloric acid.
-After this reaction was complete, it took 6.45ml of 0.0500M sodium hydroxide solution to neutralize the left over acid.
Calculate the percentage of ammonia in the cloudy ammonia.

[kakar0t]

n(NaOH)used = 0.00645 L * 0.0500M = 0.000323 mol

since 1:1 ratio then n(NaOH)used = n(NH3)present in solution

0.000323 mol in 20.00 ml
0.000323 mol * (250/20) =0.00404 mol in 250 mL

convert to mass

m(NH3) = 0.00404 mol * 17 g mol-1 = 0.0686 g

% ammonia = 0.0686g/10.213g * 100 =0.672%

I'd please ask the kind vcenoters to check my working because i'm only 90% confident.

[sanam]

LEGEND!
NOW i kno where i went wrong! thanks heaps

[kakar0t]

LEGEND!
NOW i kno where i went wrong! thanks heaps

You're welcome man

[AskQuestions]

n(NaOH)used = 0.00645 L * 0.0500M = 0.000323 mol

since 1:1 ratio then n(NaOH)used = n(NH3)present in solution

0.000323 mol in 20.00 ml
0.000323 mol * (250/20) =0.00404 mol in 250 mL

convert to mass

m(NH3) = 0.00404 mol * 17 g mol-1 = 0.0686 g

% ammonia = 0.0686g/10.213g * 100 =0.672%

I'd please ask the kind vcenoters to check my working because i'm only 90% confident.

Just a question, but isn't the 0.000323 mol the amount of leftover HCl?
So:
20.00ml of 0.105M hydrochloric acid = 0.00210 mol (n = CV).
0.00210 - 0.000323 = 0.00178 mol of reacted HCl (with NH3).
The reacted HCl reacts in a 1 to 1 ratio with the NH3.

n(NH3) = 0.00178 mol
0.00178 x 250/20 = 0.0223 mol (in 250 ml solution).
n = m/M
m = n x M
m = 0.0223 x 17.0 = 0.38 g

0.38/10.213 x 100 = 3.7 %

I'm relatively new to back titrations so i'm not sure. Could someone please confirm the answer with me?