In a laboratory experiment, a 18.0 ml sample of NaCl solution is poured into an evaporating dish with a mass of 24.00 g. The combined mass of the evaporating dish and NaCl solution is 37.15g. After heating, the evaporating dish and dry NaCl have a combined mass of 26.50 g.
If water is added to 18.0 ml of the initial NaCl solution to give a final volume of 80.0 ml, what is the molarity of the dilute NaCl solution?
(Initial Molarity of NaCl)(Initial Volume of NaCl solution)=(?)(Final Volume of diluted solution)
e.d. = evaporation dish = 24.00
mass e.d. + mass H2O + mass NaCl = 37.15g
mass e.d. + mass NaCl = 26.50
Subtract and mass H2O = 10.65
Then 24.00 + 10.65 + mass NaCl = 37.15
mass NaCl = 2.50 g
moles NaCl = grams/molar mass
M NaCl = moles NaCl/0.080 L = ??
To find the molarity of the dilute NaCl solution, we need to first calculate the number of moles of NaCl in the original solution, and then use that information to determine the molarity of the diluted solution.
1. Calculate the mass of NaCl in the original solution:
Mass of NaCl in the evaporating dish and NaCl solution = (Combined mass of evaporating dish and NaCl solution) - (Mass of empty evaporating dish)
Mass of NaCl = (37.15 g) - (24.00 g)
= 13.15 g
2. Convert the mass of NaCl to moles:
Moles of NaCl = (Mass of NaCl) / (Molar mass of NaCl)
Molar mass of NaCl = 58.44 g/mol
Moles of NaCl = (13.15 g) / (58.44 g/mol)
= 0.225 mol
3. Calculate the molarity of the original NaCl solution:
Molarity (M) = (Moles of solute) / (Volume of solution in L)
Volume of solution = 18.0 ml = 0.018 L
Molarity = (0.225 mol) / (0.018 L)
= 12.50 M
4. Calculate the final volume of the dilute NaCl solution:
Final volume = 80.0 ml = 0.08 L
5. Calculate the molarity of the dilute NaCl solution using dilution equation:
M1V1 = M2V2
(Molarity of original solution) * (Volume of original solution) = (Molarity of dilute solution) * (Final Volume)
(12.50 M) * (0.018 L) = (Molarity of dilute solution) * (0.08 L)
Solve for the Molarity of dilute solution:
(Molarity of dilute solution) = [(12.50 M) * (0.018 L)] / (0.08 L)
= 2.8125 M
Therefore, the molarity of the dilute NaCl solution is 2.8125 M.
To find the molarity of the dilute NaCl solution, we need to first determine the amount of NaCl dissolved in the initial 18.0 ml of solution.
1. First, calculate the mass of NaCl in the initial solution:
- The mass of the evaporating dish and the NaCl solution is 37.15 g.
- The mass of the evaporating dish is 24.00 g.
- Therefore, the mass of the NaCl solution alone is 37.15 g - 24.00 g = 13.15 g.
2. Next, calculate the mass of NaCl after heating:
- The mass of the evaporating dish and dry NaCl is 26.50 g.
- The mass of the evaporating dish is 24.00 g.
- Therefore, the mass of dry NaCl is 26.50 g - 24.00 g = 2.50 g.
3. Calculate the mass of dissolved NaCl:
- Initially, there was 13.15 g of NaCl in 18.0 ml of solution.
- After heating, there is 2.50 g of NaCl left.
- Therefore, the mass of dissolved NaCl is 13.15 g - 2.50 g = 10.65 g.
4. Calculate the molarity of the dilute NaCl solution:
- We know that the final volume of the solution is 80.0 ml.
- Convert the volume to liters by dividing by 1000: 80.0 ml / 1000 = 0.080 L.
- The molarity (M) of a solution is calculated using the formula: M = moles of solute / volume of solution (in liters).
- To find the moles of NaCl, divide the mass of dissolved NaCl by its molar mass, which is 58.5 g/mol.
Therefore, moles of NaCl = 10.65 g / 58.5 g/mol = 0.182 mol.
- Now substitute the moles and volume values into the molarity formula:
M = 0.182 mol / 0.080 L = 2.27 M.
Therefore, the molarity of the dilute NaCl solution is 2.27 M.