In: Chemistry
To prepare a solution of NaCl, you weight 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, with an appropriate number of digits. [Molecular mass of NaCl, 58.443 (±0.001) g/mol].
Find out the moles of NaCl weighed out = mass of NaCl weighed out/molar mass of NaCl = (2.634 g)/(58.443 g/mol) = 0.0451 mol.
Find out the molarity of the prepared NaCl solution as molarity = moles of NaCl/volume of solution in L = (0.0451 mol)/[(100.00 mL)*(1 L/1000 mL)] = (0.0451 mol)*(1000)/(100.00).(1 L) = 0.451 mol/L = 0.451 M
Next calculate the uncertainty in the measurement.
Uncertainty in mass weighed out = (0.002 g)/(2.634 g)
Uncertainty in molar mass of NaCl = (0.001 g/mol)/(58.443 g/mol)
Uncertainty in volume = (0.08 mL)/(100.00 mL)
Let the uncertainty in measurement of concentration is u(c) where c = 0.451 mol/L is the concentration.
Therefore,
[u(c)/c]2 = (0.002/2.634)2 + (0.001/58.443)2 + (0.08/100.00)2 = 1.2168*10-3
===> [u(c)/c] = √(1.2168*10-6) = 1.1031*10-3
===> u(c) = 1.1031*10-3*c = 1.1031*10-3*0.451 M = 4.975*10-4 M
The molar concentration of prepared NaCl is 0.451 0.0004975 M (ans).