por qué/ por que
  
por qué

This happens when we put the preposition por with the interrogative or exclamation qué.
In this case an accent is added to distinguish this que from the one we use to join sentences  and the one used when we talk about people and things. ( I will talk about this later since it is advanced Spanish).
Por qué introduces questions and exclamations that are direct and indirect:

¿Por qué no viniste ayer a la fiesta? ( Why didn't you come to the party?
No comprendo por qué te pones así. ( I do not comprehend why you get like this.)
¡Por qué calles más bonitas pasamos! (Why most beautiful streets we pass!)
Please note that  por qué cannot be substituted by other terms that mean reason. cause or motive.


por que

There are two ways in which  por que is used:          

1. When por  is a preposition  +  relative pronoun que. In this case, it is common to use  que with an article in front of it. (el que, la que, etc.):

Este es el motivo por (el) que te llamé. ( This the reason why I call you)   
       
Los premios por (los) que competían no resultaban muy atractivos.
(The awards for which they were competing were not very attractive)

No sabemos la verdadera razón por (la) que dijo eso.( We don't know the real reason for who said that.) 

2.In this instance, por is a preposition + que a conjunction used to join a subordinate sentence. This apears when verbs, adjectives and substantives are used before por and are followed by a sentence that is introduced by que:

Al final optaron por que no se presentase.
(In the end they chose not to submit)

Están ansiosos por que empecemos a trabajar en el proyecto.
(They are eager to begin work on the project.)

Nos confesó su preocupación por que los niños pudieran enfermar.
( He confessed his concerns that children could get sick.)

Porqué / Porque/


Porqué


It is used as an equivalent to cause, motive, reason. It is written with an accent because it is a word with a stronger phonetic accent on the last syllable. It is a substantive because it is presided by an article such as el:
no comprendo el porqué de tu actitud ( I do not understand the reason of your attitude)
  or a determinat such as su: Todo tiene su porqué.( Everything has its cause)
The plural of porqué is porqués 

Porque

It is used to introduced subordinate sentences to express cause. It can be substituted by puesto que (since) or ya que (because).
No fuí a la fiesta porque no me tenia ganas. ( I did not go to the party because I did not fill like.)
No fuí a la fiesta ya que no tenia ganas.

It is also used at the start of a response to a Why - question.
 ¿Por qué no viniste?       Why didn't you come?
Porque no tenías ganas.    Because tou did not feel like it.

When the meaning is cause , it is incorrect to write it in two words.