what type of reaction occurs when potassium metal reacts with fluorine gas?

Exothermic synthesis.

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That is Sodium and chlorine, potassium is more reactive than sodium, and fluorine is more reactive than chlorine.

2K + F2 ==> 2KF

This is a synthesis reaction.
See this for a review of different types of reactions.
http://www.usoe.k12.ut.us/CURR/science/sciber00/8th/matter/sciber/chemtype.htm

The reaction between potassium metal (K) and fluorine gas (F2) is a redox reaction or an example of an ionic compound formation. Specifically, it is a synthesis reaction or a combination reaction where two elements combine to form an ionic compound. In this case, potassium fluoride (KF) is formed. The balanced chemical equation for this reaction is:

2 K(s) + F2(g) → 2 KF(s)

When potassium metal (K) reacts with fluorine gas (F₂), it undergoes a redox reaction known as a combination or synthesis reaction. In this reaction, potassium atoms transfer their electrons to fluorine atoms.

To determine the type of reaction, follow these steps:

1. Identify the reactants and products: The reactants are potassium metal (K) and fluorine gas (F₂).
The product is potassium fluoride (KF).

2. Write the balanced chemical equation for the reaction:
2K + F₂ → 2KF

In this equation, two potassium atoms combine with one molecule of fluorine gas to form two molecules of potassium fluoride.

3. Determine the reactant that undergoes oxidation and the reactant that undergoes reduction.

In this case, potassium (K) loses one electron and forms an ion with a +1 charge: K⁺.
Fluorine (F) gains one electron and forms a fluoride ion with a -1 charge: F⁻.

Therefore, potassium is oxidized (loses electrons), and fluorine is reduced (gains electrons). This redox reaction is a combination reaction because two elements combine to form a compound.

In summary, the reaction between potassium metal and fluorine gas is a combination/synthesis reaction where potassium loses an electron and fluorine gains an electron, forming potassium fluoride.