1. A gas cylinder contains 0.722 mL of hydrogen gas at a pressure of 10.6 atm. If the gas is used to fill a balloon at a pressure of 0.960 atm, what is the volume of the filled balloon?
(10.6atm)(0.722m^3)
0.96atm = 7.97m^3
To solve this problem, we can use Boyle's Law, which states that the product of the initial pressure and volume is equal to the product of the final pressure and volume for a given amount of gas at a constant temperature.
First, let's assign the values:
Initial volume (V1) = 0.722 mL
Initial pressure (P1) = 10.6 atm
Final pressure (P2) = 0.960 atm
Final volume (V2) = ?
Using Boyle's Law, we can write:
P1 * V1 = P2 * V2
Substituting the given values:
10.6 atm * 0.722 mL = 0.960 atm * V2
Simplifying the equation:
7.6512 = 0.960 * V2
Now, we can solve for V2 by dividing both sides of the equation by 0.960:
V2 = 7.6512 / 0.960
V2 = 7.97 mL
Therefore, the volume of the filled balloon is approximately 7.97 mL.
To find the volume of the filled balloon, we can use the combined gas law. The combined gas law relates the initial and final volumes and pressures of a gas, assuming the amount of gas and temperature remain constant. The formula for the combined gas law is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures.
In this case, we are given:
P1 = 10.6 atm (initial pressure of the gas cylinder)
V1 = 0.722 mL (initial volume of the gas cylinder)
P2 = 0.960 atm (final pressure of the filled balloon)
V2 = ? (final volume of the filled balloon)
To solve for V2, we need to rearrange the formula. Cross multiplying and rearranging, we get:
V2 = (P2 * V1 * T1) / (P1 * T2)
Since we are not given the temperature, we can assume it remains constant, so T1 = T2. Therefore, we can simplify the equation to:
V2 = (P2 * V1) / P1
Now, we can substitute the given values:
V2 = (0.960 atm * 0.722 mL) / 10.6 atm
Simplifying further, we get:
V2 ≈ 0.065 mL
Therefore, the volume of the filled balloon is approximately 0.065 mL.