A balloon is filled with hydrogen at a temperature of 20 C and a pressure of 755 mmHg. If the balloons original volume was 1.05 liters, what will the new volume be at a higher altitude, where the pressure is only 625 mmHg? Assume the temperature stays the same.
p1v1 = p2v2
12.75
To find the new volume of the balloon at a higher altitude, we can use the combined gas law formula, which relates the initial and final states of a gas:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
In this case, the temperature is constant, so T1 = T2.
Let's calculate:
P1 = 755 mmHg
V1 = 1.05 liters
P2 = 625 mmHg
V2 = ?
Now we can plug the known values into the formula:
(755 mmHg * 1.05 liters) / (20 C) = (625 mmHg * V2) / (20 C)
Simplifying the equation:
(755 mmHg * 1.05 liters) = (625 mmHg * V2)
Now we can solve for V2 by dividing both sides by 625 mmHg:
V2 = (755 mmHg * 1.05 liters) / 625 mmHg
Calculating:
V2 = 1.2654 liters
Therefore, the new volume of the balloon at a higher altitude, where the pressure is only 625 mmHg, is approximately 1.2654 liters.