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Chapter 9: Problem 24

How much energy, in joules, must be absorbed to convert to \(\mathrm{Na}^{+}\) all the atoms present in \(1.00 \mathrm{mg}\) of gaseous Na? The first ionization energy of Na is \(495.8 \mathrm{kJ} / \mathrm{mol}.\)

Short Answer

Expert verified
The total energy required to convert all Sodium atoms in 1.00mg of gaseous Sodium to Sodium ions is 21.6 joules.

Step by step solution

01

Conversion of mass to moles

First, convert the mass of Sodium given to moles. Sodium has a molar mass of approximately 23g/mol. Since the given mass is presented in milligrams, it must be converted to grams first. So, 1.00mg is equivalent to 0.001g. Therefore, the number of moles of Sodium (\(Na\)) can be calculated using the formula: number of moles = given mass / molar mass = 0.001g / 23g/mol = \(4.35 x 10^{-5}\) moles
02

Calculate the energy required

The first ionization energy of Sodium (\(Na\)) is given as 495.8 kJ/mol. This is the energy required to convert 1 mole of Sodium to Sodium ions (\(Na^{+}\)). Therefore, the total energy required to ionize the given amount of Sodium can be calculated by multiplying the ionization energy with the number of moles. Therefore, Energy required = ionization energy x number of moles = 495.8 kJ/mol x \(4.35 x 10^{-5}\) moles = \(0.0216 \) kJ. To convert this to joules, multiply by 1000 (as there are 1000 joules in a kilojoule). Therefore, the total energy required is \(0.0216 \) kJ x 1000 = 21.6 joules.

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Most popular questions from this chapter

The masses of individual atoms can be determined with great precision, yet there is considerable uncertainty about the exact size of an atom. Explain why this is the case.

Briefly describe each of the following ideas or phenomena: (a) the periodic law; (b) ionization energy; (c) electron affinity; (d) paramagnetism.

Which of the following species would you expect tobe diamagnetic and which paramagnetic? (a) \(\mathrm{K}^{+}=\) (b) \(\mathrm{Cr}^{3+} ;\) (c) \(\mathrm{Zn}^{2+} ;\) (d) \(\mathrm{Cd} ;\) (e) \(\mathrm{Co}^{3+} ;\) (f) \(\mathrm{Sn}^{2+} ;\) (g) Br.

Write electron configurations to show the first two ionizations for Cs. Explain why the second ionization energy is much greater than the first.

Describe how the ionization energies of the ions \(\mathrm{He}^{-}, \mathrm{Li}^{-}, \mathrm{Be}^{-}, \mathrm{B}^{-}, \mathrm{C}^{-}, \mathrm{N}^{-}, \mathrm{O}^{-},\) and \(\mathrm{F}^{-}\) vary with atomic number.
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