Question

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

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

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

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.

Key concepts

First Ionization Energy

Ionization energy is the energy required to remove an electron from an atom or ion in its gaseous state. It's a measure of how strongly an atom holds onto its electrons. In this context, the first ionization energy refers to the energy needed to remove the outermost electron from a neutral atom. For sodium (Na), this energy is 495.8 kJ/mol.
The first ionization energy varies across elements in the periodic table. It generally increases across a period from left to right due to increasing nuclear charge, which holds onto the electrons more tightly. Conversely, it tends to decrease down a group as the electrons are further from the nucleus, making them easier to remove.
This concept helps explain why it's easier to remove an electron from sodium than from atoms like chlorine, which has a higher ionization energy. By understanding ionization energy, you can predict the reactivity of elements. Generally, elements with lower ionization energies lose electrons more readily and are more reactive, especially metals like sodium.

Molar Mass

Molar mass connects the mass of a substance to the amount of substance. It is the mass of one mole of a given element or compound, expressed in grams per mole (g/mol). For sodium, the molar mass is approximately 23 g/mol. This means one mole of sodium atoms weighs about 23 grams.
To solve chemical problems like the one in the exercise, converting the mass of sodium into moles is essential. By knowing the molar mass, you can relate the mass of a substance to the number of atoms or molecules it contains. This conversion is fundamental in stoichiometry and helps in calculations such as finding out how much energy is needed to ionize a specific amount of sodium.
When working with small quantities, such as milligrams, remember to convert into grams first before using the molar mass for calculations. This ensures accurate conversion into moles, crucial for deriving correct energy requirements or other chemical attributes.

Sodium Ionization Process

Sodium ionization involves removing an electron from a sodium atom to form a sodium ion, represented as \(\mathrm{Na}^+\). This process requires energy, known as ionization energy, and results in the creation of a positive ion from a neutral atom.
In our exercise, we explored how much energy is needed to ionize 1 mg of gaseous sodium. The strategy involves first converting the mass of sodium into moles using its molar mass. Once we know the number of moles, we can calculate the total energy needed using the first ionization energy.
The sodium ionization process is a vital concept in understanding how sodium behaves chemically. When sodium loses an electron, it attains a stable electron configuration, similar to the noble gas neon. This is why sodium tends to form positive ions readily, playing a crucial role in chemical reactions, especially in forming ionic compounds.