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Chapter 13: Problem 97

The maximum allowable concentration of lead in drinking water is 9.0 ppb. (a) Calculate the molarity of lead in a 9.0ppb solution. (b) How many grams of lead are in a swimming pool containing 9.0 ppb lead in \(60 \mathrm{~m}^{3}\) of water?

Short Answer

Expert verified
The molarity of lead in a 9.0 ppb solution is \(9.0 \times 10^{-9} M\). The mass of lead in a swimming pool containing 9.0 ppb lead in 60 m³ of water is approximately 0.011 g.

Step by step solution

01

Convert ppb to molarity

First, we need to convert the given concentration in ppb (parts per billion) to molarity. The value of 9.0 ppb can be expressed as: 9.0 ppb = 9.0 x 10^{-9} Now we need to convert this fraction to molarity. The formula for molarity (M) is: \[ M = \frac{moles}{volume~in~liters} \] we can rearrange the formula as: \[ moles = M \times volume~in~liters \] In this problem, we are considering 1 liter of solution and m_n, as the number of moles in 1 liter of solution: \[ m_n = (9.0 \times 10^{-9}) \times 1 \]
02

Calculate molarity

Now that we have the number of moles per liter, we can find the molarity. Since we calculated the moles present in 1 liter of solution, the molarity is just the moles itself: Molarity of lead = \( m_n = 9.0 \times 10^{-9} \: M \) So, the molarity of lead in a 9.0 ppb solution is \(9.0 \times 10^{-9} M\).
03

Convert m³ to liters

Now, we want to find the mass of lead in a swimming pool containing 60 m³ of water. First, we need to convert the volume of water from m³ to liters. 1 m³ = 1000 liters So, 60 m³ = 60 × 1000 = 60,000 liters
04

Calculate moles and mass of lead

We will use the molarity (M) we calculated earlier to find the moles of lead in the swimming pool: Moles of lead = Molarity × Volume in liters Moles of lead = \( (9.0 \times 10^{-9} M) \times 60,000 L \) To find the mass of lead, we can use the molar mass of lead (Pb), which is 207.2 g/mol: Mass of lead = Moles of lead × Molar mass of lead
05

Final result

Now we have all the information needed to find the mass of lead in the swimming pool: Mass of lead = [\( (9.0 \times 10^{-9} M) \times 60,000 L \)] × 207.2 g/mol So, the mass of lead in the swimming pool containing 9.0 ppb lead in 60 m³ of water is approximately 0.011 g.

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Most popular questions from this chapter

The following table presents the solubilities of several gases in water at \(25^{\circ} \mathrm{C}\) under a total pressure of gas and water vapor of 101.3 kPa. (a) What volume of \(\mathrm{CH}_{4}(g)\) under standard conditions of temperature and pressure is contained in \(4.0 \mathrm{~L}\) of a saturated solution at \(25^{\circ} \mathrm{C} ?\) (b) The solubilities (in water) of the hydrocarbons are as follows: methane \(<\) ethane \(<\) ethylene. Is this because ethylene is the most polar molecule? (c) What intermolecular interactions can these hydrocarbons have with water? (d) Draw the Lewis dot structures for the three hydrocarbons. Which of these hydrocarbons possess \(\pi\) bonds? Based on their solubilities, would you say \(\pi\) bonds are more or less polarizable than \(\sigma\) bonds? (e) Explain why NO is more soluble in water than either \(\mathrm{N}_{2}\) or \(\mathrm{O}_{2} .\) (f) \(\mathrm{H}_{2} \mathrm{~S}\) is more water-soluble than almost all the other gases in table. What intermolecular forces is $\mathrm{H}_{2} \mathrm{~S}\( likely to have with water? \)(\mathbf{g}) \mathrm{SO}_{2}$ is by far the most water-soluble gas in table. What intermolecular forces is \(\mathrm{SO}_{2}\) likely to have with water? $$ \begin{array}{lc} \hline \text { Gas } & \text { Solubility (mM) } \\ \hline \mathrm{CH}_{4} \text { (methane) } & 1.3 \\ \mathrm{C}_{2} \mathrm{H}_{6} \text { (ethane) } & 1.8 \\ \mathrm{C}_{2} \mathrm{H}_{4} \text { (ethylene) } & 4.7 \\ \mathrm{~N}_{2} & 0.6 \\ \mathrm{O}_{2} & 1.2 \\ \mathrm{NO} & 1.9 \\ \mathrm{H}_{2} \mathrm{~S} & 99 \\ \mathrm{SO}_{2} & 1476 \\ \hline \end{array} $$

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Indicate whether each statement is true or false: (a) If you compare the solubility of a gas in water at two different temperatures, you find the gas is more soluble at the lower temperature. (b) The solubility of most ionic solids in water decreases as the temperature of the solution increases. (c) The solubility of most gases in water decreases as the temperature increases because water is breaking its hydrogen bonding to the gas molecules as the temperature is raised. (d) Some ionic solids become less soluble in water as the temperature is raised.
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