A sample of helium gas initially at 37.0 degrees C, 785 torr and 2.00 L was heated to 58.0 degrees C while the volume expanded to 3.24 L. What is the final pressure in atm?
a)1.79
b)3.21
c)0.681
d).517
e)none of the above
please explain--I need to know how to do this--this is a practice problem--I don't understand.
d) should read 517, not .517
To solve this problem, we can use the combined gas law equation:
(P1 × V1) / (T1) = (P2 × V2) / (T2)
Where:
P1 = initial pressure (in torr)
V1 = initial volume (in liters)
T1 = initial temperature (in Kelvin)
P2 = final pressure (we need to find this)
V2 = final volume (in liters)
T2 = final temperature (in Kelvin)
First, we need to convert the initial and final temperatures from degrees Celsius to Kelvin. The conversion from Celsius to Kelvin is done by adding 273.15.
Initial temperature (T1) = 37.0 + 273.15 = 310.15 K
Final temperature (T2) = 58.0 + 273.15 = 331.15 K
Now, we can plug in the values into the combined gas law equation:
(785 torr × 2.00 L) / (310.15 K) = (P2 × 3.24 L) / (331.15 K)
Next, we can rearrange the equation to solve for P2:
P2 = [(785 torr × 2.00 L) / (310.15 K)] × (331.15 K / 3.24 L)
Calculating the above expression gives us:
P2 ≈ 509 torr
To convert torr to atm, we divide the pressure by 760:
P2 ≈ 509 torr / 760 torr/atm ≈ 0.67 atm
Therefore, the final pressure is approximately 0.67 atm.
None of the given answer choices match the calculated final pressure, so the correct answer is "e) none of the above."
To determine the final pressure of the helium gas, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, you need to convert the initial and final temperatures from Celsius to Kelvin. The temperature in Kelvin can be calculated using the formula T(°C) + 273.15 = T(K).
Initial temperature (Ti) = 37.0 °C + 273.15 = 310.15 K
Final temperature (Tf) = 58.0 °C + 273.15 = 331.15 K
Next, you can rearrange the ideal gas law equation to solve for P, as follows:
P = (nRT) / V
Since the number of moles of the gas (n) and the gas constant (R) are constant, and the volume is changing, you can use the ratio of the initial and final volumes to find the final pressure.
Initial pressure (Pi) = 785 torr
Initial volume (Vi) = 2.00 L
Final volume (Vf) = 3.24 L
Now, you can set up a proportion using the initial and final volumes as follows:
(Vi / Pi) = (Vf / Pf)
Rearranging the equation to solve for Pf:
Pf = (Pi * Vf) / Vi
Substituting the given values:
Pf = (785 torr * 3.24 L) / 2.00 L
Pf ≈ 1274.2 torr
Finally, convert the pressure from torr to atm by dividing by the conversion factor:
Pf = 1274.2 torr / 760 torr/atm (since 1 atm = 760 torr)
Pf ≈ 1.6747 atm
The final pressure is approximately 1.6747 atm.
Among the given options, the closest answer to the calculated value is 1.79 atm (option a).