Final answer:
Using the combined gas law, the volume of a helium-filled balloon at STP can be calculated by equating the initial and final states of pressure, volume, and temperature. The final volume (V2) can be found using the formula (P1 × V1 × T2) / (T1 × P2), with initial and final conditions plugged in for a helium-filled balloon.
Step-by-step explanation:
The question involves using the ideal gas law to calculate the volume of a helium-filled balloon at standard temperature and pressure (STP). To solve this problem, we can use the combined gas law, which is derived from the ideal gas law and relates pressure, volume, and temperature of a fixed amount of gas. The formula for the combined gas law is (P1 × V1) / T1 = (P2 × V2) / T2, where P is pressure, V is volume, and T is temperature (in Kelvin), with the subscript 1 referring to initial conditions and the subscript 2 to final conditions.
At STP, the temperature is 0°C (273.15 K) and the pressure is 101.3 kPa. Using the given information for the initial conditions: V1 = 3.40 dm³, P1 = 120.0 kPa, and T1 = 25.0°C (298.15 K), we can rearrange the equation to solve for V2, the volume of the balloon at STP: V2 = (P1 × V1 × T2) / (T1 × P2). Substituting the values will give us the answer after unit conversion if needed.