To prepare a solution of NaCl, you weigh out 2.634 (0.002)g and dissolve it in a volumetric flask whose volume is 100.00 (0.08) mL. Express the molarity of the solution, along with its uncertainty.
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To calculate the molarity of a solution, you need to know the amount of solute (in moles) and the volume of the solution (in liters). In this case, you are given the mass of the solute in grams and the volume of the solution in milliliters.
To find the amount of NaCl in moles, you need to use its molar mass. The molar mass of NaCl is approximately 58.44 g/mol.
First, let's calculate the amount of NaCl in moles using the mass and molar mass:
Amount of NaCl (in moles) = Mass of NaCl (in grams) / Molar mass of NaCl
Amount of NaCl = 2.634 g / 58.44 g/mol ≈ 0.045 moles
Now, we need to convert the volume of the solution from milliliters to liters:
Volume of the solution (in liters) = Volume of the solution (in milliliters) / 1000
Volume of the solution = 100.00 mL / 1000 = 0.100 liters
Finally, we can calculate the molarity of the solution:
Molarity (M) = Amount of NaCl (in moles) / Volume of the solution (in liters)
Molarity = 0.045 moles / 0.100 liters ≈ 0.45 M
Now let's calculate the uncertainty in the molarity. You were given an uncertainty in the mass (±0.002 g) and an uncertainty in the volume (±0.08 mL).
To find the uncertainty in the amount of NaCl, you can use the following formula:
Uncertainty in the amount of NaCl = Mass of NaCl × (Uncertainty in mass / Mass of NaCl)
Uncertainty in the amount of NaCl = 2.634 g × (0.002 g / 2.634 g) ≈ 0.002 g
To find the uncertainty in the volume of the solution, you can use the following formula:
Uncertainty in the volume of the solution = Volume of the solution × (Uncertainty in volume / Volume of the solution)
Uncertainty in the volume of the solution = 100.00 mL × (0.08 mL / 100.00 mL) ≈ 0.08 mL
Now, let's find the uncertainty in molarity using these uncertainties:
Uncertainty in molarity = (Uncertainty in the amount of NaCl / Amount of NaCl) + (Uncertainty in the volume of the solution / Volume of the solution)
Uncertainty in molarity = (0.002 g / 2.634 g) + (0.08 mL / 100.00 mL) ≈ 0.00076
Therefore, the molarity of the NaCl solution is approximately 0.45 M, with an uncertainty of ±0.00076 M.