'an air of desperation' is a correct and usable phrase in written English. You can use this phrase when describing a feeling or atmosphere which has a sense of urgency, such as when describing a situation of hopelessness. Example sentence: As I entered the room, I could sense an air of desperation from those gathered there.
The changes suggested an air of desperation.
"There was really an air of desperation.
Regular guys get to play!" -- has an air of desperation.
Still, there is an air of desperation about Netanyahu's defiance.
No one believes that the crisis is over; an air of desperation lingers.
With tree-clearing finally underway, an air of desperation is gripping opponents.
Good projects get funded by it, but there's an air of desperation about it.
However, Bowie's quest for new sounds to plunder began to evince an air of desperation.
The manager's responsible for that," the goalkeeper Sebastian Mielitz said with an air of desperation.
Mr. Spiegelman said it now has an "air of desperation and tiredness".
Pundits interpreted an air of desperation in the quote, which came after 10 straight wins for Obama.
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Retail Lead Linguist @ Apple Inc.