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Chapter 21: Problem 30

How many electrons does \(1.00 \mathrm{~kg}\) of water contain?

Short Answer

Expert verified
Answer: In 1 kg of water, there are approximately \(3.34\times10^{26}\) electrons.

Step by step solution

01

Determine the molar mass of water

The molar mass of water, H2O, can be calculated by adding up the molar masses of its constituent atoms: 2 hydrogen atoms and 1 oxygen atom. The molar mass of hydrogen is about 1 g/mol, and the molar mass of oxygen is about 16 g/mol. So the molar mass of water is: \(1 \mathrm{~g/mol} *2 + 16\mathrm{~g/mol} = 18\mathrm{~g/mol}\)
02

Convert mass of water to moles

To convert 1 kg (1000 g) of water to moles, divide the mass by the molar mass: \(\text{moles of water} = \frac{1000\mathrm{~g}}{18\mathrm{~g/mol}} = 55.56\mathrm{~mol}\)
03

Calculate the number of water molecules

Next, we will use Avogadro's number (\(6.022\times10^{23}\)) to convert moles of water into individual water molecules: \(\text{water molecules} = 55.56\mathrm{~mol} \times 6.022\times10^{23}\mathrm{~molecules/mol} \approx 3.34\times10^{25}\mathrm{~molecules}\)
04

Determine the number of electrons in 1 water molecule

A water molecule (H2O) contains 2 hydrogen atoms and 1 oxygen atom. Since hydrogen atoms have 1 electron each and oxygen atoms have 8 electrons each, the total number of electrons in a water molecule is: \(1\times2 + 8\times1 = 10\mathrm{~electrons}\)
05

Calculate the total number of electrons

Finally, multiply the number of water molecules in 1 kg of water by the number of electrons in each water molecule to find the total number of electrons: \(\text{total electrons} = 3.34\times10^{25}\mathrm{~molecules} \times 10\mathrm{~electrons/molecule} = 3.34\times10^{26}\mathrm{~electrons}\) In 1 kg of water, there are approximately \(3.34\times10^{26}\) electrons.

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Most popular questions from this chapter

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