Answer :
To solve this problem, we need to determine two things:
(a) the molar concentration of the ammonia in the solution, and
(b) the mass/mass percent concentration of ammonia.
Let's go step-by-step:
### (a) Calculate the molar concentration of the ammonia
1. Determine the moles of [tex]\(HNO_3\)[/tex] used in the reaction:
- Volume of [tex]\(HNO_3\)[/tex] used: [tex]\(25.10 \, \text{mL}\)[/tex]
- Concentration of [tex]\(HNO_3\)[/tex]: [tex]\(0.245 \, \text{M}\)[/tex]
Convert the volume from mL to L:
[tex]\[ 25.10 \, \text{mL} = 0.02510 \, \text{L} \][/tex]
Calculate the moles of [tex]\(HNO_3\)[/tex]:
[tex]\[ \text{Moles of } HNO_3 = \text{Concentration} \times \text{Volume} = 0.245 \, \text{M} \times 0.02510 \, \text{L} = 0.0061495 \, \text{mol} \][/tex]
2. Determine the moles of [tex]\(NH_3\)[/tex] that reacted:
From the balanced chemical equation:
[tex]\[ HNO_3(aq) + NH_3(aq) \rightarrow NH_4NO_3(aq) \][/tex]
The stoichiometry is 1:1, meaning 1 mole of [tex]\(HNO_3\)[/tex] reacts with 1 mole of [tex]\(NH_3\)[/tex]. Hence, the moles of [tex]\(NH_3\)[/tex] are the same as the moles of [tex]\(HNO_3\)[/tex]:
[tex]\[ \text{Moles of } NH_3 = 0.0061495 \, \text{mol} \][/tex]
3. Calculate the molar concentration of [tex]\(NH_3\)[/tex]:
- Volume of ammonia solution: [tex]\(10.0 \, \text{mL}\)[/tex]
Convert the volume from mL to L:
[tex]\[ 10.0 \, \text{mL} = 0.0100 \, \text{L} \][/tex]
Calculate the molar concentration:
[tex]\[ \text{Molar concentration of } NH_3 = \frac{\text{Moles of } NH_3}{\text{Volume of solution in L}} = \frac{0.0061495 \, \text{mol}}{0.0100 \, \text{L}} = 0.61495 \, \text{M} \][/tex]
### (b) Calculate the mass/mass percent concentration of ammonia
1. Calculate the mass of [tex]\(NH_3\)[/tex] in the solution:
- Molar mass of [tex]\(NH_3\)[/tex]: [tex]\(17.04 \, \text{g/mol}\)[/tex]
Calculate the mass:
[tex]\[ \text{Mass of } NH_3 = \text{Moles of } NH_3 \times \text{Molar mass} = 0.0061495 \, \text{mol} \times 17.04 \, \text{g/mol} = 0.10482528 \, \text{g} \][/tex]
2. Calculate the total mass of the ammonia solution:
- Volume of ammonia solution: [tex]\(10.0 \, \text{mL}\)[/tex]
- Density of ammonia solution: [tex]\(0.985 \, \text{g/mL}\)[/tex]
Calculate the total mass:
[tex]\[ \text{Total mass of the solution} = \text{Volume} \times \text{Density} = 10.0 \, \text{mL} \times 0.985 \, \text{g/mL} = 9.85 \, \text{g} \][/tex]
3. Calculate the mass/mass percent concentration:
[tex]\[ \text{Mass/mass percent concentration} = \left( \frac{\text{Mass of } NH_3}{\text{Mass of the solution}} \right) \times 100 = \left( \frac{0.10482528 \, \text{g}}{9.85 \, \text{g}} \right) \times 100 = 1.0638322842639594 \% \][/tex]
### Final Answers:
(a) The molar concentration of the ammonia is [tex]\(0.61495 \, \text{M}\)[/tex].
(b) The mass/mass percent concentration of ammonia is [tex]\(1.06383 \%\)[/tex].
(a) the molar concentration of the ammonia in the solution, and
(b) the mass/mass percent concentration of ammonia.
Let's go step-by-step:
### (a) Calculate the molar concentration of the ammonia
1. Determine the moles of [tex]\(HNO_3\)[/tex] used in the reaction:
- Volume of [tex]\(HNO_3\)[/tex] used: [tex]\(25.10 \, \text{mL}\)[/tex]
- Concentration of [tex]\(HNO_3\)[/tex]: [tex]\(0.245 \, \text{M}\)[/tex]
Convert the volume from mL to L:
[tex]\[ 25.10 \, \text{mL} = 0.02510 \, \text{L} \][/tex]
Calculate the moles of [tex]\(HNO_3\)[/tex]:
[tex]\[ \text{Moles of } HNO_3 = \text{Concentration} \times \text{Volume} = 0.245 \, \text{M} \times 0.02510 \, \text{L} = 0.0061495 \, \text{mol} \][/tex]
2. Determine the moles of [tex]\(NH_3\)[/tex] that reacted:
From the balanced chemical equation:
[tex]\[ HNO_3(aq) + NH_3(aq) \rightarrow NH_4NO_3(aq) \][/tex]
The stoichiometry is 1:1, meaning 1 mole of [tex]\(HNO_3\)[/tex] reacts with 1 mole of [tex]\(NH_3\)[/tex]. Hence, the moles of [tex]\(NH_3\)[/tex] are the same as the moles of [tex]\(HNO_3\)[/tex]:
[tex]\[ \text{Moles of } NH_3 = 0.0061495 \, \text{mol} \][/tex]
3. Calculate the molar concentration of [tex]\(NH_3\)[/tex]:
- Volume of ammonia solution: [tex]\(10.0 \, \text{mL}\)[/tex]
Convert the volume from mL to L:
[tex]\[ 10.0 \, \text{mL} = 0.0100 \, \text{L} \][/tex]
Calculate the molar concentration:
[tex]\[ \text{Molar concentration of } NH_3 = \frac{\text{Moles of } NH_3}{\text{Volume of solution in L}} = \frac{0.0061495 \, \text{mol}}{0.0100 \, \text{L}} = 0.61495 \, \text{M} \][/tex]
### (b) Calculate the mass/mass percent concentration of ammonia
1. Calculate the mass of [tex]\(NH_3\)[/tex] in the solution:
- Molar mass of [tex]\(NH_3\)[/tex]: [tex]\(17.04 \, \text{g/mol}\)[/tex]
Calculate the mass:
[tex]\[ \text{Mass of } NH_3 = \text{Moles of } NH_3 \times \text{Molar mass} = 0.0061495 \, \text{mol} \times 17.04 \, \text{g/mol} = 0.10482528 \, \text{g} \][/tex]
2. Calculate the total mass of the ammonia solution:
- Volume of ammonia solution: [tex]\(10.0 \, \text{mL}\)[/tex]
- Density of ammonia solution: [tex]\(0.985 \, \text{g/mL}\)[/tex]
Calculate the total mass:
[tex]\[ \text{Total mass of the solution} = \text{Volume} \times \text{Density} = 10.0 \, \text{mL} \times 0.985 \, \text{g/mL} = 9.85 \, \text{g} \][/tex]
3. Calculate the mass/mass percent concentration:
[tex]\[ \text{Mass/mass percent concentration} = \left( \frac{\text{Mass of } NH_3}{\text{Mass of the solution}} \right) \times 100 = \left( \frac{0.10482528 \, \text{g}}{9.85 \, \text{g}} \right) \times 100 = 1.0638322842639594 \% \][/tex]
### Final Answers:
(a) The molar concentration of the ammonia is [tex]\(0.61495 \, \text{M}\)[/tex].
(b) The mass/mass percent concentration of ammonia is [tex]\(1.06383 \%\)[/tex].
