A 1.00 mL sample of N2(g) at 36.2 oC and 2.14 atm is heated to 37.8 oC, and the pressure changed to 1.02 atm. What volume does the gas occupy at this final temperature and pressure?
A cylinder contains a gas at 5.25 atm pressure. When the gas is allowed to
expand to a final volume of 12.5 L, the pressure drops to 1.85 atm. What was
the original volume of the gas?
For the first question, use P1V1/T1 = P2V2/T2 Remember to use kelvin for T; i.e., Kelvin = 273 + C.
For #2 use P1V1 = P2V2
Post your work if you get stuck.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
First, let's convert the temperatures from Celsius to Kelvin:
T1 = 36.2 oC = 36.2 + 273.15 = 309.35 K
T2 = 37.8 oC = 37.8 + 273.15 = 311.95 K
Next, we need to calculate the number of moles (n) of the gas. We can use the ideal gas law equation to do that.
Rearranging the equation, we have:
n = PV / RT
For the initial conditions:
P1 = 2.14 atm
V1 = 1.00 mL = 1.00 cm^3
T1 = 309.35 K
Now, we can calculate n1:
n1 = (P1 * V1) / (R * T1)
Using the values in the equation, we have:
n1 = (2.14 atm * 1.00 cm^3) / (0.0821 L * atm / K * mol * 309.35 K)
n1 ≈ 0.00009018 mol
Now, let's calculate the final volume (V2) using the ideal gas law equation with the new pressure and temperature.
P2 = 1.02 atm
T2 = 311.95 K
Rearranging the equation, we have:
V2 = (n2 * R * T2) / P2
Substituting the values, we get:
V2 = (0.00009018 mol * 0.0821 L * atm / K * mol * 311.95 K) / 1.02 atm
V2 ≈ 0.00236 L
Therefore, the gas occupies approximately 0.00236 L at the final temperature and pressure.
To solve this question, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
We can solve for the volume (V) by rearranging the equation as follows:
V = (nRT) / P
Now, let's compute the volume of the gas at the final temperature and pressure.
First, convert the temperatures from Celsius to Kelvin:
Initial temperature (T1) = 36.2 + 273.15 = 309.35 K
Final temperature (T2) = 37.8 + 273.15 = 311.95 K
Next, convert the pressures from atm to Pascal:
Initial pressure (P1) = 2.14 atm * 101325 Pa/atm = 216959.5 Pa
Final pressure (P2) = 1.02 atm * 101325 Pa/atm = 103381.25 Pa
Now, let's find the volume:
We'll assume the number of moles (n) remains constant.
V1 = V2
(nRT1) / P1 = (nRT2) / P2
Since the number of moles cancels out, we can rearrange and solve for V2:
V2 = (V1 * P2 * T1) / (P1 * T2)
Substituting the known values:
V2 = (1.00 mL * 0.001 L/mL * 103381.25 Pa * 309.35 K) / (216959.5 Pa * 311.95 K)
After performing the calculations, the volume, V2, should be in liters.