You are confronted with an unknown metal, M, and need to determine its identity. Using the following information identify the metal.

M(s) Reacts vigorously with water and acid.

M(s) does not react with K+(aq)

M(s) reacts with Co+2(aq)

M(s) does not react with Ca+2(s)

M(s) reacts with Na+(aq)

In order to identify the unknown metal, we need to analyze its reactivity with different substances. Let's break down the given information step by step:

1. Reacts vigorously with water and acid: This indicates that the metal reacts with water to produce a metal hydroxide and hydrogen gas (M + H2O → MOH + H2). Additionally, the metal reacts with acids to produce a salt and hydrogen gas (M + 2HCl → MCl2 + H2). This suggests that the metal is an active metal.

2. Does not react with K+(aq): If the metal does not react with K+(aq) (potassium ions), it suggests that the metal is less reactive than potassium. This narrows down our options because metals with higher reactivity than potassium should displace it in a reaction.

3. Reacts with Co+2(aq): The metal reacts with Co+2(aq) (cobalt ions), which means that the metal is more reactive than cobalt. This further reduces the possibilities of the metal's identity.

4. Does not react with Ca+2(s): The metal does not react with Ca+2(s) (calcium ions) in solid state. This implies that the metal is less reactive than calcium.

5. Reacts with Na+(aq): The metal reacts with Na+(aq) (sodium ions). This indicates that the metal is more reactive than sodium.

Based on the given information, we can conclude that the metal M is more reactive than sodium (Na), but less reactive than calcium (Ca). Additionally, it is more reactive than cobalt (Co) and potassium (K). One metal that fits these characteristics is magnesium (Mg).

To verify this conclusion, you can perform additional tests to confirm the reactivity and characteristics of the unknown metal. These tests could include further reactions with different substances or conducting physical and chemical analyses using techniques such as spectroscopy.