Is zakat obligatory on money collected in a charity box, and if so, is it 2.5% of the money for each year, with the remainder given as charity?

Money designated for charity and placed in a special box does not cease to be the property of its owner until it reaches the poor. Therefore, you are both obligated to pay zakat (definition) on this money for the past years at a rate of 2.5% annually, if it reached the nisab (definition) and a hawl passed over it. This mixed money is considered as one fund, and after paying the zakat, you have the choice to donate what remains or to benefit from it. The former and more complete option is to donate it.