Cyclopropane, C3H6 is a general anesthetic. A 6.0-L sample has a pressure of 5.2 atm.
What is the final volume, in liters, of this gas given to a patient at a pressure of 1.0 atm with no change in temperature and amount of gas? Express your answer using two significant figures
According to Boyle's Law, the relationship between pressure and volume for a fixed amount of gas at a constant temperature is P1 * V1 = P2 * V2.
We can use this equation to solve for the final volume (V2):
P1 * V1 = P2 * V2
(5.2 atm) * (6.0 L) = (1.0 atm) * V2
Now, we can solve for V2:
V2 = (5.2 atm * 6.0 L) / 1.0 atm
V2 = 31.2 L
Therefore, the final volume of the gas is 31.2 liters.
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, as long as the temperature and amount of gas remain constant.
Mathematically, we can express this as:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
We are given:
P1 = 5.2 atm
V1 = 6.0 L
P2 = 1.0 atm
Substituting these values into the equation, we can solve for V2:
5.2 atm * 6.0 L = 1.0 atm * V2
31.2 L atm = V2
Therefore, the final volume is 31.2 L (rounded to two significant figures).
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 if the temperature and amount of gas remain constant.
According to Boyle's Law:
P1 * V1 = P2 * V2
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume
In this case, the initial pressure (P1) is 5.2 atm, the initial volume (V1) is 6.0 L, the final pressure (P2) is 1.0 atm, and we need to find the final volume (V2).
Rearranging the formula, we get:
V2 = (P1 * V1) / P2
Substituting the given values, we have:
V2 = (5.2 atm * 6.0 L) / 1.0 atm
Calculating this, we find:
V2 = 31.2 L
Thus, the final volume of the gas administered to the patient at a pressure of 1.0 atm (with no change in temperature and amount of gas) is 31.2 liters.