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Chapter 18: Problem 93

If the \(\mathrm{pH}\) of a 1.0 -in. rainfall over \(1500 \mathrm{mi}^{2}\) is 3.5 , how many kilograms of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) are present, assuming that it is the only acid contributing to the \(\mathrm{pH}\) ?

Short Answer

Expert verified
The mass of H2SO4 in the rainfall is calculated as follows: Moles of H2SO4 = \(\frac{10^{-3.5}}{2}\) * \(9.889 \times 10^8 \, L\) Mass of H2SO4 = Moles of H2SO4 * 98 g/mol Mass of H2SO4 (kg) = Mass of H2SO4 (g) * \(10^{-3} \, kg/g\) After calculating these values, we can determine the mass of H2SO4 in kilograms present in the rainfall.

Step by step solution

01

Find the concentration of H+ ions from the given pH value

We're given that the pH of the rainfall is 3.5. The equation to find the concentration of H+ ions is: \(pH = -\log[H^+]\) Now, let's calculate the concentration of H+ ions: \([H^+] = 10^{-pH}\) \[ [H^+] = 10^{-3.5} \]
02

Find moles of H2SO4 in the solution assuming it's the only acid

Since H2SO4 is the only acid contributing to the pH, we can assume the molarity of H2SO4 is equal to the concentration of H+ ions we calculated in Step 1. The stoichiometry between H2SO4 and H+ ions is a 1:2 ratio, therefore the molarity of H2SO4 will be half the concentration of H+ ions. Moles of H2SO4: \[ [H_2SO_4] = \frac{[H^+]}{2}\] \[ [H_2SO_4] = \frac{10^{-3.5}}{2} \]
03

Convert the rainfall volume to liters

We're given a 1.0-inch rainfall over 1500 sq. miles. To find the total volume of rainfall in liters, we need to convert the given values: 1 inch = 2.54 cm 1 mile = 1.609 km First, convert the area from square miles to square centimeters: \[1500 \, mi^2 * (1.609 \times 10^5 \, cm/mi)^2 = 3.89 \times 10^{11} \, cm^2\] Next, find the volume in cubic centimeters: \(V = 1.0 \, in * 3.89 \times 10^{11} \, cm^2 * (2.54 \, cm/in) = 9.889 \times 10^{11} \, cm^3\) Lastly, convert the volume to liters: \(V = 9.889 \times 10^{11} \, cm^3 * (0.001 \, L/cm^3) = 9.889 \times 10^{8} \, L\)
04

Calculate the mass of H2SO4 in the solution

Now that we have the molarity of H2SO4 and the volume of the solution, we can calculate the mass of H2SO4: Moles of H2SO4 = Molarity * Volume Moles of H2SO4 = \(\frac{10^{-3.5}}{2}\) * \(9.889 \times 10^8 \, L\) Molecular weight of H2SO4 = 98 g/mol Mass of H2SO4 = Moles of H2SO4 * Molecular Weight Mass of H2SO4 = Moles of H2SO4 * 98 g/mol Convert the mass to kilograms: Mass of H2SO4 (kg) = Mass of H2SO4 (g) * \(10^{-3} \, kg/g\)
05

Final Answer

Calculate the mass of H2SO4 in kilograms using the above formulas to find the amount of H2SO4 in the rainfall.

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