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You are preparing a solution and you record the following data.                Mass of NaCl = 9.93 g ± 0.01 g                Volume of volumetric flask = 200.00 cm3 ± 0.15 cm3M  NaCl = 58.44 g mol–1What is the correct concentration of the solution together with the absolute uncertainty?

Question

You are preparing a solution and you record the following data.                Mass of NaCl = 9.93 g ± 0.01 g                Volume of volumetric flask = 200.00 cm3 ± 0.15 cm3M  NaCl = 58.44 g mol–1What is the correct concentration of the solution together with the absolute uncertainty?

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Solution

To calculate the concentration of the solution, we first need to find the number of moles of NaCl. This can be done using the formula:

Number of moles = mass / molar mass

Substituting the given values:

Number of moles = 9.93 g / 58.44 g mol–1 = 0.170 mol

The concentration (C) of the solution can be calculated using the formula:

C = number of moles / volume

Substituting the given values:

C = 0.170 mol / 200.00 cm3 = 0.00085 mol/cm3

To convert this to a more standard unit (mol/L), we multiply by 1000 (since 1 L = 1000 cm3):

C = 0.00085 mol/cm3 * 1000 = 0.85 mol/L

Now, to calculate the absolute uncertainty, we use the formula:

Absolute uncertainty = (uncertainty in measurement / measurement) * calculated value

For the mass of NaCl:

Absolute uncertainty = (0.01 g / 9.93 g) * 0.85 mol/L = 0.00086 mol/L

For the volume of the volumetric flask:

Absolute uncertainty = (0.15 cm3 / 200.00 cm3) * 0.85 mol/L = 0.00064 mol/L

Adding these two uncertainties together gives the total absolute uncertainty:

Total absolute uncertainty = 0.00086 mol/L + 0.00064 mol/L = 0.0015 mol/L

So, the concentration of the solution is 0.85 mol/L ± 0.0015 mol/L.

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