Question

please answer all three questions

1.) The US Safe Drinking Water Act requires the US EPA regulate contaminates in drinking water.
Bromate ion is a carcinogen that is produced as a by-product of water disinfection, and the bromate ion
concentration in finished drinking water can be no higher than 0.010 mg/L as an annual average.
Calculate the annual average limit for bromate ion in terms of a.) ppb and b.) molarity. Assume that the
density of drinking water is 1 g/mL.

2.) Acid rain has been a point of contention between the US and Canada partly because some of the acid
is the result of sulfur dioxide emissions by coal-fired power plants. The sulfur dioxide dissolves in rain
water and forms sulfuric acid, which decreases the pH of rain water. If the coal that is combusted
averages 2% sulfur by weight, how many metric tons of coal would be required to yield enough H2SO4 to
produce 1 inch of rainfall with a pH of 4.00 over a 104 mile2 area?

3.) If everyone in the world planted a tree today, how long would it take for these trees to decrease the
concentration of CO2 by 1 ppm? Assume that 9 kg of O2 is produced per tree each year regardless of age,
and the CO2 and H2O combine through photosynthesis to form biomass (C6H12O6) and O2. Also assume
that the CO2 that can be assimilated is only in troposphere, which extends 17 km above the surface of the
Earth, and the average temperature and pressure of the troposphere are 273 K and 0.6 atm, respectively

Answer 1

1.(a)  Given the concentration of bromate ion(BrO₃^-) = 0.010 mg/L = 0.010 mg x (1g / 1000 mg) / L = 1.0 x 10^-5 g/L

1 ppb = 1x10^-9 g/m3 = 1 microgram / L

Hence concentration of  bromate ion(BrO₃^-) in terms of ppb = 1.0 x 10^-5 g/L = 10 microgram/L = 10 ppb (answer)

(b) Given the concentration of bromate ion(BrO₃^-) = 0.010 mg/L = 0.010 mg x (1g / 1000 mg) / L = 1.0 x 10^-5 g/L

Hence 1.0 x 10^-5 g of  bromate ion(BrO₃^-) is present in 1L of water.

Molecular mass of  bromate ion(BrO₃^-) = 127.90 g.mol^-1

Hence moles of bromate ion(BrO₃^-) present in 1L = mass / mlecular mass

= 1.0 x 10^-5 g / 127.90 g.mol^-1 = 7.82 x 10^-8 mol

Hence annual average of bromate ion in terms of molarity =  7.82 x 10^-8 mol / L (answer)

Q.2: Volume of rain water having pH 4 = 1 inch x 104 mile²

= 1 inch x (0.0254 m / 1 inch) x 104 mile² x (2.59 x 10⁶ m² / 1 mile²) = 6.8417x10⁶ m3 = 6.8417x10⁹ L

pH = - log[H⁺(aq)] = 4

=> [H⁺(aq)] = 10^-4 M

Hence 1 L of water contains the moles of H⁺ ion =  10^-4 mol

Hence  6.8417x10⁹ L water that contains the moles of H⁺ ion = 10^-4 mol/L x 6.8417x10⁹ L

= 6.8417x10⁵ mol H⁺ ion

Since H2SO4 is a dibasic acid, 2 moles of H⁺ ion are present in 1 mol of H2SO4.

Hence  6.8417x10⁵ mol H⁺ ion that would be present in the moles of H2SO4

= (1 mol H2SO4 / 2 mol H⁺ ion) x 6.8417x10⁵ mol H⁺ ion = 3.421 x 10⁵ mol H2SO4

Molecular mass of H2SO4 = 98.079 g/mol

Hence mass of H2SO4 in the rain = 3.421 x 10⁵ mol x 98.079 g/mol

= 3.355 x 10⁷ g = 3.355 x 10⁷ g x ( 1 metric ton / 10⁶ g) = 33.55 metric ton H2SO4

SO3 + H2O ---- > H2SO4

1 mol ---------------- 1 mol

1 mol of SO3 is required to produce 1 mol of H2SO4.

Hence 33.55 metric ton of SO3 is required to produce 33.55 metric ton of H2SO4.

Also 1 mole of S-atom will produce 1 mol of SO3. Hence 33.55 metric ton of S is required to produce the desired amount of H2SO4.

Given the coal contains 2% S by weight.

Hence the mass of coal required to burn = 33.55 metric ton S x (100 / 2) = 1677.5 metric ton coal (answer)