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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

You bring a negatively charged rubber rod close to a grounded conductor without touching it. Then you disconnect the ground. What is the sign of the charge on the conductor after you remove the charged rod? a) negative d) cannot be determined from b) positive the given information c) no charge

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