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Chapter 3: Problem 97

A public water supply was found to contain 1 part per billion (ppb) by mass of chloroform, \(\mathrm{CHCl}_{3}\) (a) How many \(\mathrm{CHCl}_{3}\) molecules would be present in a \(225 \mathrm{mL}\) glass of this water? (b) If the \(\mathrm{CHCl}_{3}\) in part (a) could be isolated, would this quantity be detectable on an ordinary analytical balance that measures mass with a precision of ±0.0001 g?

Short Answer

Expert verified
The number of \(\mathrm{CHCl}_{3}\) molecules present in a \(225 \mathrm{mL}\) glass of this water is approximately \(1.13 \times 10^{15}\) and this quantity is not detectable on an ordinary analytical balance that measures mass with a precision of ±0.0001 g since the calculated mass of chloroform is far less than the balance precision.

Step by step solution

01

Calculate the mass of water

Determine the mass of the 225 mL glass of water. Since the density of water is approximately \(1 \mathrm{g/mL}\), the mass of this volume of water equals to the volume in mL. So, it would be approximately \(225 \mathrm{g}\).
02

Calculate the mass of chloroform

Calculate the mass of chloroform in the water sample. Since there's 1 ppb (part-per-billion) by mass of chloroform, it means there's 1 gram of chloroform per billion grams of water. Hence, the amount of \(\mathrm{CHCl}_{3}\) in our sample is \(225 \cdot 10^{-9} \mathrm{g}\).
03

Calculate the number of molecules

Find out the number of chloroform molecules in the given mass. First, we need to know the molar mass of \(\mathrm{CHCl}_{3}\) which is \(119.37 \mathrm{g/mol}\), then convert mass to moles using the molar mass. The quantity in moles is \((225 \cdot 10^{-9}) / 119.37\). In order to find out the number of molecules, multiply the mole quantity by Avogadro's number \(6.022 \times 10^{23} / \mathrm{mol}\).
04

Comparison with balance precision

Check if the obtained mass of chloroform is detectable by the balance. Compare the calculated mass of \(\mathrm{CHCl}_{3}\) with the precision of the balance which is \(0.0001 \mathrm{g}\). If the mass of \(\mathrm{CHCl}_{3}\) is greater than or equal to the balance precision, it would be detectable.

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Most popular questions from this chapter

A formula unit of the compound \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{SO}_{4}\) has nearly equal masses of (a) \(\mathrm{S}\) and \(\mathrm{O} ;\) (b) \(\mathrm{N}\) and \(\mathrm{O}\) (c) \(\mathrm{H}\) and \(\mathrm{N} ;\) (d) \(\mathrm{Cu}\) and \(\mathrm{O}\)

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