A 51.46 mL sample of an ammonia solution is analyzed by titration with HCl. The reaction is given below.

NH3(aq) + H+(aq) NH4+(aq)
It took 38.57 mL of 0.0984 M HCl to titrate (react completely with) the ammonia. What is the concentration of the original ammonia solution?

moles HCl = M x L = ??

moles NH3 = moles HCl (from the equation--it is a 1:1 reaction ratio)
M NH3 = moles NH3/L NH3.

To determine the concentration of the original ammonia solution, you can use the stoichiometry of the reaction and the volume and concentration of the HCl solution used.

1. Write the balanced equation for the reaction:
NH3(aq) + H+(aq) → NH4+(aq)

2. Use the stoichiometry of the reaction to determine the moles of NH3 reacted:
From the balanced equation, the stoichiometric ratio between NH3 and HCl is 1:1. Therefore, the moles of NH3 reacted is equal to the moles of HCl used.

Moles of HCl = Volume of HCl used (L) × Concentration of HCl (M)
Moles of HCl = (38.57 mL ÷ 1000 mL/L) × 0.0984 M

3. Convert the moles of HCl to moles of NH3:
Since the stoichiometric ratio is 1:1, the moles of NH3 reacted is the same as the moles of HCl used.

4. Calculate the concentration of the original ammonia solution:
Concentration of NH3 (M) = Moles of NH3 ÷ Volume of ammonia solution (L)
Concentration of NH3 = Moles of NH3 ÷ (51.46 mL ÷ 1000 mL/L)

Substitute the values calculated previously:
Concentration of NH3 = Moles of HCl ÷ (51.46 mL ÷ 1000 mL/L)

Calculate the value:
Concentration of NH3 = [((38.57 mL × 0.0984 M) ÷ 1000 mL/L)] ÷ (51.46 mL ÷ 1000 mL/L)

Solve the equation to find the concentration of the original ammonia solution.

By following these steps, you should be able to calculate the concentration of the original ammonia solution.

To find the concentration of the original ammonia solution, we can use the concept of stoichiometry and the volume and concentration of the HCl solution.

Here are the steps to solve this problem:

Step 1: Write and balance the equation for the reaction between ammonia (NH3) and hydrochloric acid (HCl):
NH3(aq) + H+(aq) -> NH4+(aq)

Step 2: Write the balanced chemical equation in terms of moles:
1 mole of NH3 reacts with 1 mole of H+

Step 3: Calculate the number of moles of HCl used in the titration:
moles of HCl = volume of HCl solution (L) x concentration of HCl (M)
moles of HCl = 0.03857 L x 0.0984 M

Step 4: Use stoichiometry to relate moles of HCl to moles of NH3:
moles of NH3 = moles of HCl

Step 5: Calculate the concentration of the original ammonia solution:
concentration of NH3 = moles of NH3 / volume of ammonia solution (L)
concentration of NH3 = moles of NH3 / 0.05146 L

By substituting the values into the formula, the concentration of the original ammonia solution can be calculated.