Using Charles's Law, we know that the volume of a gas is proportional to the temperature of the gas, assuming a constant pressure. We can use this relationship to solve the problem.
First, we need to calculate the temperature at which the balloon will reach its maximum volume before bursting. We can use the following equation:
(V1/T1) = (V2/T2)
where V1 is the initial volume of the gas, T1 is the initial temperature, V2 is the maximum volume of the gas before bursting, and T2 is the temperature at which the gas will reach its maximum volume.
Plugging in the values we know, we get:
(1.28 L)/(2°C + 273.15) = (1.50 L)/(T2 + 273.15)
Simplifying this equation, we get:
T2 = [(1.50 L)(2°C + 273.15)]/(1.28 L) - 273.15
T2 = 305.7 K - 273.15
T2 = 32.55°C
Therefore, the temperature at which the balloon will burst is 32.55°C.