You can store information in a gas, but you can't store much.
Gasses are really inconvenient for this job, because they are always trying to escape from whatever container they're stored in, getting molecules stuck to the walls, and so on. They also move around at great speed. So counting molecules is impractical. Temperature, pressure and volume are almost completely interchangeable with gasses, so you can't store information in those separately: they really only amount to a single value "how much gas is there?" and that changes, fractionally, due to leaks.
The reactions between the different kinds of gas in a mixture aren't very useful because they'll either have gone to completion, in which case it's just two numbers, amount of gas A and amount of gas B, or they're in equilibrium, in which case you have three gasses to have amounts of, but the amounts change with temperature.
The presence or absence of different gasses, as read by a sense of smell, is your best bet, since such a sense can detect lots of different organic compounds, but this is still a very low-density way of storing information compared to DNA, and it isn't a good long-term means, because the sensor will interact with the gas and contaminate it slightly.
The thing that makes DNA storage so excellent is that it's built around long chain molecules. Very highly organised matter like that gives you very dense storage. But you can't have long chain molecules in a gas, because of their high molecular weight: before you get them hot enough to be a gas, they fall apart.
You might get lasting information storage of a kilobit per cubic centimetre with a scent-based mechanism. DNA, in an experiment in 2012, gave storage of 5.5 petabits per cubic millimetre, about 5 million million million times as dense. No, those three "million"s in a row aren't a mistake.