To solve this problem, we need to use the ideal gas law, which relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas:
PV = nRT
where R is the universal gas constant.
Assuming that the number of moles and the pressure of the gas remain constant, we can write:
V1/T1 = V2/T2
where V1 is the initial volume of the balloon, T1 is the initial temperature, V2 is the final volume of the balloon, and T2 is the final temperature.
Plugging in the given values:
V1 = 4.21 L
T1 = 25.0 °C + 273.15 = 298.15 K (converting to Kelvin)
T2 = 50.0 °C + 273.15 = 323.15 K (converting to Kelvin)
We can solve for V2:
V2 = V1 x T2/T1
V2 = 4.21 L x (323.15 K / 298.15 K)
V2 = 4.21 L x 1.084
V2 = 4.56 L (rounded to two decimal places)
Therefore, the volume of the balloon will be 4.56 L when the temperature is 50.0°C.