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)

To identify the unknown metal M, we will analyze its reactions with different substances. From the information provided, we have the following observations:

1. M(s) reacts vigorously with water and acid.
This suggests that the metal M is likely an active metal that readily reacts with both water and acids.

2. M(s) does not react with K+(aq).
The lack of reaction between M(s) and K+(aq) indicates that M is not a metal that displaces potassium from its aqueous solution.

3. M(s) reacts with Co+2(aq).
The fact that M(s) reacts with Co+2(aq) suggests that M is a metal that displaces cobalt from its aqueous solution.

4. M(s) does not react with Ca+2(s).
The lack of reaction between M(s) and Ca+2(s) indicates that M is not a metal that displaces calcium from its solid form.

5. M(s) reacts with Na+(aq).
The reaction between M(s) and Na+(aq) suggests that M is a metal that displaces sodium from its aqueous solution.

Considering all the observations, the likely identity of the unknown metal M is a metal that is more reactive than potassium, cobalt, calcium, and sodium. Based on these characteristics, the metal M could potentially be a very reactive metal like lithium (Li), which matches all the observations given.

To confirm the identity of the metal M, further tests such as flame test or chemical analysis could be performed.