A 2.300×10 2 M solution of NaCl in water is at 20.0C. The sample was created by

Question

A 2.300×102M solution of NaCl in water is at 20.0C. The sample was created by dissolving a sample of NaCl in water and then bringing the volume up to 1.000 L. It was determined that the volume of water needed to do this was 999.4 mL . The density of water at 20.0C is 0.9982 g/mL.

A: Calculate the molarity of the salt solution.

B: Calculate the mole fraction of salt in this solution.

C: Calculate the concentration of the salt solution in percent by mass.

D: Calculate the concentration of the salt solution in parts per million.

Your help is GREATLY appreciated!

Explanation / Answer

A 2.300×102M solution of NaCl in water is at 20.0C. The sample was created by dissolving a sample of NaCl in water and then bringing the volume up to 1.000 L. It was determined that the volume of water needed to do this was 999.4 mL . The density of water at 20.0C is 0.9982 g/mL.

Given : Molarity of NaCl solution = 2.300 E -2 M

Volume of solution= 1.000 L

Volume of water = 999.4 mL

Density of water = 0.9982 g /mL

A: Calculate the molarity of the salt solution.

Molarity of the solution given in the problem and that is = 2.300 E -10 M

B: Calculate the mole fraction of salt in this solution.

We know mole fraction of the solute =mol solute / (mol solute + solvent)

We calculate moles of solute by using molarity and volume in L

Molarity = mol of solute / volume of solution in L

Mol solute = volume of solution * molarity of the solute

= 1.000 L * 2.300 E-2 M

= 2.300 E -2 mol NaCl

Now we calculate moles of solvent(water )

To calculate moles of water we need calculate its mass.

Mass of water can be found by using density and volume.

Density= mass / volume

Mass = density * volume

= 0.9982 g /mL * 999.4 mL

=997.6 g

Mol H2O = Mass of H2O in g / Molar mass of H2O

Molar mass of H2O = 18.0148 g /mol

Mol H2O = 997.6 g / 18.0148 g per mol

= 55.38 mol

Mol fraction of NaCl = 2.300E-2 mol / ( 2.300 E-2 + 55.38) mol

= 4.152 E-4

C: Calculate the concentration of the salt solution in percent by mass.

Mass percent of solute = Mass of solute / ( Mass of solution )

Mass of solute = moles of solute * molar mass of solute

= 2.300 E-2 mol * 58.443 g per mol

= 1.344 g NaCl

Mass of water =997.6 g

Mass of solution = 1.344 g NaCl + 997.6 g H2O = 998.9 g

Mass percent of NaCl = (1.344 / 998.9 ) * 100

= 0.13 %

D: Calculate the concentration of the salt solution in parts per million.

Ppm = ( Mass of solute in g / Mass of solution in g ) * 1.000 E6

=(1.344 / 998.9 ) * 1.000 /E6

= 1346.0 ppm

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