What law was created in order to keep a balance of power between slave and free states in the union

The Missouri Compromise was passed in 1820, and established the 36°30′ north line of latitude as the boundry - States south of this would be slave states, states north of it (With the exception of Missouri) would be free states.

This became problematic, however, as several issues came up, such as:

A) A movement to let the states decide for themselves, which turned out to be what was done and the Missouri Compromise was repealed in 1857, (it actually was ruled as Unconstitutional in Dred Scott vs Sandford)

B) California - It's in the middle and on both sides of the line, and it was admitted as a Free State in the Compromise of 1850, which, more or less repealed the Missouri Compromise as the rules it establishes were thrown out, a deal was made establishing California as a free state in return for a slave Texas and a stricter fugitive slave law.