A solution is prepared by dissolving 10.8 g of ammonium nitrate in enough water to make 100.0 mL of solution. A 10.0 mL portion of this sample is diluted to 50.0 mL total volume. What is the molarity of the final solution?
a number of ways to do this
he must have put 1/10 of 10.8g in the sample, then diluted it to a volume of .050liters
Molarity=10.8/10 * 1/molmass*1/.050
where molmass is the molmass of ammonium nitrate.
To find the molarity of the final solution, we need to first calculate the number of moles of ammonium nitrate in the 10.0 mL portion of the sample.
1. Calculate the number of moles of ammonium nitrate in the 10.0 mL portion:
- Given mass of ammonium nitrate: 10.8 g
- Molar mass of ammonium nitrate (NH4NO3):
- NH4 = 1(14.01 g/mol) = 14.01 g/mol
- NO3 = 1 (14.01 g/mol) + 3(16.00 g/mol) = 62.01 g/mol
- NH4NO3 = 14.01 g/mol + 62.01 g/mol = 76.02 g/mol
- Moles of ammonium nitrate = Mass / Molar mass
- Moles = 10.8 g / 76.02 g/mol =~ 0.142 moles
2. Calculate the molarity of the 10.0 mL portion:
- Molarity (M) = Moles of solute / Liters of solution
- Moles of solute = 0.142 moles
- Liters of solution = 10.0 mL * (1 L / 1000 mL) = 0.010 L
- Molarity = 0.142 moles / 0.010 L =~ 14.20 M
3. Calculate the final molarity after dilution:
- Initial volume = 10.0 mL
- Final volume = 50.0 mL
- Initial molarity = 14.20 M
- Dilution formula: (Minitial)(Vinitial) = (Mfinal)(Vfinal)
- (14.20 M)(10.0 mL) = (Mfinal)(50.0 mL)
- (14.20 M)(0.010 L) = (Mfinal)(0.050 L)
- 0.142 M = (Mfinal)(0.050 L)
- Mfinal = 0.142 M / 0.050 L
- Mfinal =~ 2.84 M
Therefore, the molarity of the final solution is approximately 2.84 M.
To determine the molarity of the final solution, we need to first calculate the number of moles of ammonium nitrate in the original solution, and then use that value to calculate the molarity of the final solution.
Step 1: Calculate the number of moles of ammonium nitrate in the original solution.
The molar mass of ammonium nitrate (NH4NO3) is:
NH4NO3 = 14.01 g/mol (molar mass of nitrogen) + 4(1.01 g/mol) + 3(16.00 g/mol) = 80.04 g/mol
To find the number of moles, we divide the mass of ammonium nitrate by its molar mass:
Number of moles = Mass / Molar mass
Number of moles = 10.8 g / 80.04 g/mol
Number of moles = 0.135 mol (rounded to three decimal places)
Step 2: Calculate the molarity of the final solution.
Molarity is defined as the number of moles of solute (ammonium nitrate) divided by the volume of the solution in liters.
First, we need to calculate the number of moles of ammonium nitrate in the diluted sample.
Moles in diluted sample = Moles in original solution x (Volume of diluted sample / Volume of original solution)
Moles in diluted sample = 0.135 mol x (10.0 mL / 100.0 mL)
Moles in diluted sample = 0.0135 mol (rounded to four decimal places)
Next, we calculate the molarity of the final solution:
Molarity = Moles of solute (ammonium nitrate) / Volume of solution (in liters)
Molarity = 0.0135 mol / 0.050 L
Molarity = 0.27 mol/L (rounded to two decimal places)
Therefore, the molarity of the final solution is 0.27 mol/L.