Final answer:
Using Boyle's Law, which states that pressure and volume are inversely proportional at constant temperature, the new volume of the balloon when the pressure is increased to 3.00 atmospheres at 22C is calculated to be 1.67 liters.
Step-by-step explanation:
The student's question involves the change of a balloon's volume under different pressure conditions at a constant temperature, which is described by Boyle's Law. Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is kept constant. Therefore, the volume of the gas decreases as the pressure increases and vice versa. Given that the initial conditions are a volume of 5.00 liters at 1.00 atmosphere of pressure, we can use the formula P1V1 = P2V2 to find the new volume (V2) when the pressure (P2) is increased to 3.00 atmospheres while temperature remains constant at 22C.
Initial conditions:
P1 = 1.00 atm
V1 = 5.00 L
Final conditions:
P2 = 3.00 atm
V2 = ? L
Using Boyle's Law, we solve for V2:
P1V1 = P2V2
1.00 atm × 5.00 L = 3.00 atm × V2
V2 = (1.00 atm × 5.00 L) / 3.00 atm
V2 = 5.00 L / 3
V2 = 1.67 L