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Module 4: Liquid Characteristics - Concentration - Practice Problems

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Instructions:
Work these problems on a sheet of paper and check your answers against those provided below.

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#1
The concentration of cadmium (Cd) in a liquid is known to be 130 ppm at 20°C. Calculate the total quantity of cadmium present in a one-gallon sample. Assume a specific gravity of 1.0(20°C/4°C Ref. T).

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Answer: 0.00108 lbm Cd

Solution:

  1. Calculate the density of the sample using the following equation.

    Practice Equation 1(1)

  2. Calculate the total mass of the one-gallon sample.

    Practice Equation 1(2)

  3. Calculate the total mass of cadmium in the one-gallon sample using the following equation.

    Practice Equation 1(3)

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#2
As a quality control check, a sample of acetone is taken from a process to determine the concentration of suspended particulate matter. An 850-mL sample was placed in a beaker and evaporated. The remaining suspended solids were determined to have a mass of 0.001 gm.

The specific gravity of acetone is 0.79 (4°C/4°C Ref. T).

  1. Determine the concentration of the sample as mg/L.

  2. Determine the concentration of the sample as ppm.

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Answer: i. 1.18 mg/L

Solution:

Practice Equation 2i

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Answer: ii. 1.49 ppm

Solution:
Use the following equation to solve the problem. Since the mass of solute is negligible, it can be ignored in the denominator.

Practice Equation 2ii

  1. From the specific gravity of acetone, determine its density in units of gm/cm3.

    Practice Equation 2(1)

  2. Determine the mass of the acetone in grams.

    Practice Equation 2(2)

  3. Use equation above to determine the concentration in ppm.

    Practice Equation 2(3)

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#3
A paper mill produces paper from wood pulp. Pulp production (at the pulp plant) begins with digesting the wood chips in a solution of sodium hydroxide and sodium sulfide. The sodium hydroxide is diluted with water (shown in the reaction below) prior to being sent to the digester.

Practice Equation 3

If 4 kg of sodium hydroxide is added for each 1000 L of water, determine the following:

  1. The molarity of the resulting solution.

  2. The normality of the resulting solution.

Link to periodic table of elements.

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Answer: i. 0.1 M NaOH

Solution:
The mass of the sodium hydroxide is negligible compared to the mass of the water and can be ignored in the denominator.

Practice Equation 3i

  1. Calculate the approximate molecular weight (MW) of NaOH.

    Practice Equation 3i(1)

  2. Calculate the molarity of the NaOH solution.

    Practice Equation 3i(2)

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Answer: ii. 0.1 N NaOH

Solution:

Practice Equation 3ii

  1. Calculate the equivalent weight of NaOH.

    Practice Equation 3ii(1)

  2. Calculate the number of gram equivalent weights of NaOH.

    Practice Equation 3ii(2)

  3. Calculate the normality.

    Practice Equation 3ii(3)

Note: Normality and molarity concentrations are equivalent since the change in oxidation number is 1.

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Q icon #4
If the concentration of mercury (Hg) in water is 0.25 ppm at 20°C, what is its concentration in mg/L at the same temperature? The density of mercury is 13.6 gm/cm3 at 20°C.

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Answer: 0.250 mg/L

Solution:

  1. Assuming a basis of 1,000,000 gm of solution, convert 0.25 ppm of mercury to its equivalent mass ratio (in gm).

    Practice Equation 4(1)

  2. Calculate the volume of the water in liters. Recall that the density of pure water is 1 gm/cm3.

    Practice Equation 4(2)

  3. Using the density data, calculate the volume of mercury in liters.

    Practice Equation 4(3)

  4. Calculate the concentration of the mercury and water solution in mg/L.

    Practice Equation 4(4)

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