A very flexible helium-filled balloon is released from the ground into the air at 20. ∘ C . The initial volume of the balloon is 5.00 L , and the pressure is 760. mmHg . The balloon ascends to an altitude of 20 km , where the pressure is 76.0 mmHg and the temperature is − 50. ∘ C . What is the new volume, V 2 , of the balloon in liters, assuming it doesn't break or leak?
(p1v1/t1) = (p2v2/t2)
You have p1 and p2, v1 and you need v2, you have t1 and t2. Substitute and solve for v2. Remember to convert the t1 and t2 to kelvin. To do that K = 273 + C = ?
Post your work if you get stuck.
To find the new volume (V2) of the balloon at an altitude of 20 km, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure = 760 mmHg
V1 = initial volume = 5.00 L
T1 = initial temperature = 20°C + 273.15 = 293.15 K
P2 = final pressure = 76.0 mmHg
T2 = final temperature = -50°C + 273.15 = 223.15 K
Now, let's plug in the values into the equation and solve for V2:
(760 mmHg * 5.00 L) / (293.15 K) = (76.0 mmHg * V2) / (223.15 K)
Cross-multiplying the equation, we get:
(760 mmHg * 5.00 L * 223.15 K) = (76.0 mmHg * V2 * 293.15 K)
Simplifying the equation:
V2 = (760 mmHg * 5.00 L * 223.15 K) / (76.0 mmHg * 293.15 K)
V2 ≈ 3.112 L
Therefore, the new volume (V2) of the balloon at an altitude of 20 km is approximately 3.112 liters.
To find the new volume of the balloon, we can use the combined gas law, which relates the initial and final conditions of temperature, pressure, and volume.
The combined gas law formula is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
- P1 and P2 are the initial and final pressures, respectively
- V1 and V2 are the initial and final volumes, respectively
- T1 and T2 are the initial and final temperatures, respectively
Given:
- P1 = 760 mmHg (pressure at the ground)
- V1 = 5.00 L (initial volume)
- T1 = 20 °C (initial temperature)
- P2 = 76.0 mmHg (pressure at 20 km altitude)
- T2 = -50 °C (temperature at 20 km altitude)
We need to convert temperatures from Celsius to Kelvin, as the gas laws require temperature to be in Kelvin.
T1 = 20 + 273.15 = 293.15 K
T2 = -50 + 273.15 = 223.15 K
Now, let's plug in the values into the combined gas law formula:
(760 mmHg * 5.00 L) / 293.15 K = (76.0 mmHg * V2) / 223.15 K
To find V2, we can rearrange the formula:
V2 = (760 mmHg * 5.00 L * 223.15 K) / (293.15 K * 76.0 mmHg)
Now, let's perform the calculation:
V2 = (1136780 mmHg * L * K) / (22320.4 mmHg * K)
V2 = 50.85 L
Therefore, the new volume, V2, of the balloon is approximately 50.85 liters.