The fact that your seeds are heirlooms has nothing to do with how long it takes for them to sprout. The fact that they are "old" does affect how long it takes and even whether they sprout at all. Even fresh seeds don't always sprout. Older seeds usually take a little longer. So people usually plant more seeds than they want since germination rates can be low. Each kind of seed takes a different amount of time and requires different conditions. Fresh romaine and arugula can sprout in 3 to 7 days in cool conditions. Older sunflower seeds may take up to two weeks and require warmer conditions.

How old are your seeds and how have they been stored? Some seeds can stay viable for more than 10 years. But if they dry out, they usually die.