A patient's oxygen tank holds 23.8 L of oxygen (02) at a pressure of 13.6 atm.
What is the final volume, in liters, of this gas when it is released at a pressure of 1.06 atm with no change in temperature and amount of gas?
Express your answer with the appropriate units.
We can use the combined gas law to solve this problem. The combined gas law equation is:
P1V1/T1 = P2V2/T2
Since the temperature and amount of gas remain constant, we can eliminate the T1 and T2 terms from the equation. Rearranging the equation, we have:
P1V1 = P2V2
Plugging in the given values:
(13.6 atm)(23.8 L) = (1.06 atm)(V2)
Solving for V2:
V2 = (13.6 atm)(23.8 L) / (1.06 atm) = 305.64 L
Therefore, the final volume of the gas is 305.64 L.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature and amount of gas.
Boyle's Law formula: P1V1 = P2V2
Given:
Initial pressure (P1) = 13.6 atm
Initial volume (V1) = 23.8 L
Final pressure (P2) = 1.06 atm
Final volume (V2) = ?
Substituting the given values into the Boyle's Law formula, we get:
13.6 atm * 23.8 L = 1.06 atm * V2
Simplifying the equation:
322.08 atm*L = 1.06 atm * V2
To isolate V2, we can divide both sides of the equation by 1.06 atm:
322.08 atm*L / 1.06 atm = V2
Dividing the left side of the equation gives us the final answer:
V2 = 303.77 L
Therefore, the final volume of the gas when released at a pressure of 1.06 atm is 303.77 L.
To find the final volume of the gas, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature and amount of gas are constant.
Boyle's Law formula is given as:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
P2 = final pressure of the gas
V2 = final volume of the gas
In this case, we are given:
P1 = 13.6 atm
V1 = 23.8 L
P2 = 1.06 atm
We need to solve for V2.
Plugging in the given values into the formula, we can solve for V2:
(13.6 atm) * (23.8 L) = (1.06 atm) * V2
Dividing both sides of the equation by 1.06 atm, we can isolate V2:
V2 = (13.6 atm * 23.8 L) / (1.06 atm)
Calculating this expression:
V2 = 311.62 L
Therefore, the final volume of the gas when released at a pressure of 1.06 atm is 311.62 liters.