The volume of a gas is 5.80 L, measured at 1.00 atm. What is the pressure of the gas in mmHg if the volume is changed to 9.65 L? (The temperature remains constant.)
constant temp (Boyles law)
P*9.65L=760mmHg*5.80
PV is a constant. solve for P
To find the pressure of the gas in mmHg when the volume changes from 5.80 L to 9.65 L while the temperature remains constant, we can use Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional when the temperature is constant.
Boyle's Law can be stated as:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure (in atm)
V1 = initial volume (in L)
P2 = final pressure (to be found)
V2 = final volume (in L)
In this case, the initial pressure (P1) is given as 1.00 atm, the initial volume (V1) is 5.80 L, and the final volume (V2) is 9.65 L.
Plugging in these values into the Boyle's Law equation, we get:
1.00 atm * 5.80 L = P2 * 9.65 L
Now, we can solve for P2, which is the pressure we are trying to find.
P2 = (1.00 atm * 5.80 L) / 9.65 L
Calculating this, we find:
P2 ≈ 0.612 atm
To convert the pressure from atm to mmHg, we can use the conversion factor 1 atm = 760 mmHg.
Converting P2 from atm to mmHg:
P2 = 0.612 atm * 760 mmHg/atm
Calculating this, we get:
P2 ≈ 465.12 mmHg
Therefore, the pressure of the gas in mmHg when the volume is changed to 9.65 L is approximately 465.12 mmHg.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is constant.
Boyle's Law formula: P1V1 = P2V2
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
Based on the given information, we have:
P1 = 1.00 atm
V1 = 5.80 L
V2 = 9.65 L (volume is changed)
Now, we can use Boyle's Law formula to find P2:
P1V1 = P2V2
Substituting the values:
(1.00 atm) * (5.80 L) = P2 * (9.65 L)
Solving for P2:
P2 = (1.00 atm) * (5.80 L) / (9.65 L)
P2 = 0.6186 atm
To convert from atm to mmHg, we can use the following conversion factor:
1 atm = 760 mmHg
Converting the pressure:
P2 = 0.6186 atm * 760 mmHg/atm
P2 ≈ 469.65 mmHg
Therefore, the pressure of the gas, when the volume is changed to 9.65 L, is approximately 469.65 mmHg.