Question

Express each aqueous concentration in the unit indicated.

a). 25 mg of trichloroethylene in 9.5 L of water, as ppb of trichloroethylene

b). 38 g Cl2 in 1.00x 104 L of water, as ppm Cl2

c). 2.4 ppm F -, as molarity of fluoride ion, in [mol F - /L]

d). 45 ppm NO3 -, as molarity of nitrate ion in [mol NO3 - /L]

e). Why do some scientists prefer to express concentrations of water contaminants in the units ppm and ppb rather than molarity?

Answer 1

a) The concentration of trichloroethylene in ppb is 25,000 ppb. b) The concentration of Cl2 in ppm is 38,000 ppm. c) The molarity of fluoride ion is 2.4 x 10^-5 mol F- /L. d) The molarity of nitrate ion is 7.26 x 10^-4 mol NO3- /L. e) Scientists prefer ppm and ppb for water contaminants because they are more relevant for trace-level contaminants and easier to understand for non-chemists.

Step-by-step explanation:

a) To express the aqueous concentration of trichloroethylene in ppb, we need to convert the given concentration of 25 mg in 9.5 L of water to ppb. Since 1 ppm is equal to 1 mg/L, 1 ppb is equivalent to 1 µg/L. Therefore, to convert mg/L to ppb, we multiply by 1000. So, the concentration of trichloroethylene in ppb is 25,000 ppb.

b) To express the aqueous concentration of Cl2 in ppm, we need to convert the given concentration of 38 g in 1.00x 104 L of water to ppm. 1 ppm is equal to 1 mg/L, so we need to convert grams to mg by multiplying by 1000. The concentration of Cl2 in ppm is therefore 38,000 ppm.

c) To express the aqueous concentration of F- in molarity, we need to convert the given concentration of 2.4 ppm to molarity. To do this, we need to convert ppm to mg/L, and then to mol/L using the molar mass of F-. The molar mass of F- is 18.998 g/mol. Converting the concentration of F- from ppm to mg/L, we multiply by 1,000,000. Therefore, the molarity of fluoride ion is 2.4 x 10^-5 mol F- /L.

d) To express the aqueous concentration of NO3- in molarity, we need to convert the given concentration of 45 ppm to molarity. To do this, we need to convert ppm to mg/L, and then to mol/L using the molar mass of NO3-. The molar mass of NO3- is 62.0049 g/mol. Converting the concentration of NO3- from ppm to mg/L, we multiply by 1,000,000. Therefore, the molarity of nitrate ion is 7.26 x 10^-4 mol NO3- /L.

e) Scientists prefer to express concentrations of water contaminants in ppm and ppb rather than molarity because these units are more relevant for trace-level contaminants. Molarity is most commonly used for solutions with higher concentrations, while ppm and ppb allow for accurate reporting of very small concentrations. Additionally, ppm and ppb provide an easier-to-understand representation of the concentration for non-chemists.

Answer 2

a. ppb of trichloroethylene = 3 × 10⁶ ppb

b. ppm of Cl₂ = 3.8 ppm

c. Molarity = 0.0002 mol / L

d. Molarity = 0.0007 mol / L

e. For trace amount of concentrations

Step-by-step explanation:

a. Given data

mass of trichloroethylene = 25 mg

Volume of water = 9.5 L

ppb of trichloroethylene = ?

Solution

As we know that

1 L = 1000 milliliters

9.5 L = 9.5 × 1000

9.5 L = 9500 millileters (ml)

we consider 25 mg = 25 millileters

ppb = (mass of solute / mass of solvent) × 1000,000,000 (1 billion)

ppb of trichloroethylene = (25 ÷ 9500) × 1000,000,000

ppb of trichloroethylene = 0.003 × 1000,000,000

ppb of trichloroethylene = 3 × 10⁶ ppb

B. Given data

Mass of Cl₂ = 38 g

volume of water = 1.00 × 10⁴ L ( 10000 L)

ppm of Cl₂ = ?

Solution

Volume of water in ml = 1 L = 1000 ml

Volume of water in ml = 10000 × 1000

Volume of water in ml = 10000000 ml

we take 38 g = 38 ml

Now we convert it to ppm

ppm = (mass of solute / mass of solvent) × 1000000 (1 million)

ppm of Cl₂ = ( 38 ÷ 10000000 ) × 1000000

ppm of Cl₂ = 0.0000038 × 1000000

ppm of Cl₂ = 3.8 ppm

C. Given data

Concentration of F⁻ ( Fluoride ion) = 2.4 ppm

Molarity = ?

Solution

As we know that 1 ppm = 0.001 g / L

2.4 ppm = 2.4 × 0.001 g/L

2.4 ppm = 0.0024 g/L

Mass of flouride ions = 0.0024 g

Now we find number of moles

moles = mass / molar mass

molar mass of F⁻ = 19 g/mol

moles of F⁻ = 0.0024 g / 19 g/mol

moles of F⁻ = 0.0002 mol

Molarity = mol of solute / liter of solution

Molarity = 0.0002 mol / 1 L

Molarity = 0.0002 mol / L

D. Given data

Concentration of NO₃⁻ ( nitrate ion) = 45 ppm

Molarity = ?

Solution

As we know that 1 ppm = 0.001 g / L

45 ppm = 45 × 0.001 g/L

45 ppm = 0.045 g/L

Mass of nitrate ions = 0.045 g

Now we find number of moles

moles = mass / molar mass

molar mass of NO₃⁻ = 62 g/mol

moles of NO₃⁻ = 0.045 g / 62 g/mol

moles of F⁻ = 0.0007 mol

Molarity = mol of solute / liter of solution

Molarity = 0.0007 mol / 1 L

Molarity = 0.0007 mol / L

E. Reason of expressing concentration in ppm and ppb

Scientist prefer ppm and ppb notations when the concentration difference of solute and solvent are very high.

As water contains contaminants is a very low amount we can say in trace amounts so scientist prefer ppm and ppb rather than molarity.

Example

Arcenic is an under ground water contaminant and its concentration of 10 μg/L is dangerous for health.

Lets change this in to molarity

mass = 10 μg

10 μg = 10 / 1000000

10 μg = 0.00001 g

now find out moles of Arcenic

moles = mass / molar mass

molar mass of arcenic = 75 g/mol

moles = mass / molar mass

moles of arcenic = 0.00001 g / 75 g/mol

moles of arcenic = 0.00000012 mol

Molarity = moles of solute / litres of solution

Molarity = 0.00000012 mol / 1 L

Molarity = 0.00000012 mol/ L

As we can see that in molarity it is a negligible amount so scientists express it in ppm and ppb