People vape for various reasons. Many do it to quit tobacco, some like the flavour, and some like just having something in their hand that they can take a puff from. It’s comforting to have a vape mod or pod in hand, and it’s that comfort that some people lean on to manage their anxiety.
Let’s dig more into how vaping can possibly help in dealing with anxiety.

It’s important that we properly define what anxiety is. Anxiety is your body's natural response to stress. It’s a feeling of apprehension and unease, either through concern or fear. Everyone has feelings of anxiety at some point in their life, either mild or severe.
People with anxiety disorders often experience excessive and persistent worry and fear in everyday situations. Anxiety disorders have repeated episodes of anxiety that get intense within minutes, resulting in panic attacks.
Anxiety disorders are difficult to control, out of proportion to the actual danger, and can be chronic. You may have to avoid places or situations to prevent attacks, and it may manifest during childhood or adolescence and go on into adulthood.
There’s generalized anxiety, social anxiety or social phobia, specific phobias, and separation anxiety. It’s possible to have more than one anxiety disorder. Sometimes, anxiety results from a different medical condition that must be treated to alleviate the resulting anxiety.

Nicotine is the main addictive chemical in tobacco. Reasons why nicotine causes anxiety are not fully understood. Current theories speculate on effects of carbon monoxide and other chemicals in cigarettes being the cause.
The chemicals in cigarettes are known to lead to lung illness, which can trigger anxiety through shortness of breath. According to WebMd, Nicotine is a stimulant, which raises heart rate and increases blood pressure.
Tobacco smoke induces airway resistance and other respiratory problems, as well as sleep problems. Sleep deprivation and shortness of breath can also lead to anxiety.

It’s common for smokers and vaper to say it calms them down. Vaping can be a comfort habit, like a hug or eating comfort food. Due to its relaxing nature, it can help with anxiety, depression, PTSD, etc. For some people, knowing they have something to calm them down or take their mind off things can help.
Vaping doesn't cause most of those problems associated with smoking. Even with lower nicotine levels, vaping can reduce stress. It can replace cigarettes altogether as vaping can be an adequate substitute for tobacco.
Mental health has a strong connection with the placebo effect. Mental health conditions can be made worse by one's ignorance, fear, or feeling of being alone. Believing that you have something that can help you feel better can have a positive effect in battling that condition.

Yes and no. Without nicotine, there's no physical “need" to vape, similar to smoking. What remains are either an oral fixation or a deliberate want to vape. It's common for people to enjoy social vaping, depending on the individual and their preferences. Doing it with other people can be comforting, thus decreasing anxiety.
Many people vape simply for flavor and smell. It can be a form of aromatherapy, which is known to help relieve stress and anxiety.
If you've completely cut nicotine or a non-smoker, vaping can help with relaxation even without nicotine. Eliquid has no harsh chemicals like in cigarettes. Nicotine-free eliquid has no actual stimulants other than caffeine in some if indicated. For most of them, no increase of heart rate or blood pressure to be expected.

It’s not a cure-all solution; not one thing can instantly cure anxiety. It’s a process of knowing about oneself, understanding when and how anxiety can strike, and what things can help manage it. In the end, vaping could be one of those minor tools in dealing with depressive episodes and a relatively safer option of managing stress.