訳(わけ)だFor that reason, No wonder, As you'd expect, Naturally, Thus, This is why

はずがない denies something based on logic or evidence, while わけだ draws a conclusion or explains a reason. For example, 来るはずがない ('There's no way he'll come.') vs. 来るわけだ ('So that's why he's coming.'). One rejects a possibility, while the other clarifies it.

Both express logical conclusions, but with different emphasis. はずだ conveys expectation or prediction, as in 来るはずだ ('He should come.'). わけだ explains a reason behind something known or observed, like 来るわけだ ('So that's why he's coming.'). はずだ leans future-oriented, わけだ explanatory.

わけだ and ため(に) are similar in that both can be used when expressing a reason, but they mean quite different things. わけだ is used when drawing a conclusion, like the English 'so that's why (A)', while ため(に) on the other hand means 'for the sake of (A)' or 'due to (A)'.

Both だけに and わけだ can be used to draw conclusions, but differ in tone and focus. だけに emphasizes an expected result based on a known condition, e.g. 忙しい人だけに来ないと思った ('Precisely because he's a busy man, I thought he wouldn't come'), while わけだ indicates the speaker's realization based on something previously expressed or observed, e.g. だから来ないわけだ ('So that's why he's not coming').

Both だけのことはある and わけだ can be used when drawing conclusions, but function differently. だけのことはある affirms that an outcome is appropriate or deserved in a positive sense, e.g. プロだけのことはある ('It's as expected from a pro'), while わけだ signals the speaker's understanding or conclusion, e.g. だから負けたわけだ ('So that's why we lost'). The latter conveys realization, in either a positive or negative sense.

Both express reasoning in a broad sense, but are used differently. わけだ explains why something is the case, e.g. 暖房が壊れているのか。だから寒いわけだ ('So the heater's broken. That explains why it's cold.') ことだ gives strong advice or instruction, e.g. 寒いなら暖房をつけることだ ('If it's cold, you should turn on the heater.')