Some commentators argue that the day of Pentecost was also associated with the giving of the law at Mount Sinai (which took place in the third month after Passover). As a result Pentecost can also be seen as a time to celebrate the inauguration of the old covenant.1 Though this idea is certainly present in some Jewish writings, there is nothing to suggest that Luke wants us to understand Pentecost through this lens.2 There is also some evidence to suggest that it was only after the destruction of the temple in 70 AD that Jews began to link Pentecost with the giving of the law.3
1 When the day of Pentecost arrived, they were all together in one place.