Final answer:
Using the combined gas law and converting the temperatures to Kelvin, we can calculate the new volume of the balloon as approximately 3.99 liters when it rises 3 kilometers, where the pressure is 0.667 atm, and the temperature is -10.0°C.
Step-by-step explanation:
The question involves applying the combined gas law, which correlates pressure, volume, and temperature of a gas. Given that a child's toy balloon has a starting volume of 2.90 liters, at a temperature of 20.0 °C, and a pressure of 1.01 atm, we can calculate the new volume when the balloon is at a height where the pressure is 0.667 atm, and the temperature is -10.0°C.
To find the new volume, we use the combined gas law formula:
P1 × V1 / T1 = P2 × V2 / T2, where P is the pressure, V is the volume, and T is the temperature in Kelvin. Converting the temperatures to Kelvin, we get 293.15 K (20.0°C) and 263.15 K (-10.0°C) for T1 and T2, respectively. We re-arrange the formula to solve for V2:
V2 = P1 × V1 × T2 / P2 × T1. Plugging in the values:
V2 = (1.01 atm × 2.90 L × 263.15 K) / (0.667 atm × 293.15 K), which simplifies to V2 ≈ 3.99 liters.
Thus, the new volume of the balloon would be approximately 3.99 liters at the altitude of 3 kilometers.