Find the pressure of a gas that originally had a volume of 25 L, pressure of 67kPa at a temperature of 100 Kelvin. When the gas was heated to 200 Kelvin, it had a volume of 56L.
How many moles would be present if the gas in the above question was an ideal gas?
For the first part, use
(P1V1/T1) = (P2V2/T2)
Solve for P2 (I guess that's what the problem is asking for. It's a funny way, and confusing way, of stating a problem.
For the second part, use any set of P, V, T, and use PV = nRT and solve for n = number of moles.
To find the number of moles present in an ideal gas, 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 the gas
R is the ideal gas constant (8.314 J/(mol*K))
T is the temperature of the gas in Kelvin
We are given:
Initial conditions:
Volume (V1) = 25 L
Pressure (P1) = 67 kPa (which needs to be converted to Pa: 1 kPa = 1000 Pa)
Temperature (T1) = 100 K
Final conditions:
Volume (V2) = 56 L
Temperature (T2) = 200 K
To find the pressure at the final conditions, we can rearrange the ideal gas law equation to solve for pressure:
P = (n * R * T) / V
We can solve for the number of moles (n) by rearranging the equation:
n = (P * V) / (R * T)
Now, let's plug in the values and calculate the number of moles:
Initial conditions:
P1 = 67 kPa = 67,000 Pa
V1 = 25 L
T1 = 100 K
Final conditions:
V2 = 56 L
T2 = 200 K
R = 8.314 J/(mol*K)
n = (P1 * V1) / (R * T1)
= (67,000 Pa * 25 L) / (8.314 J/(mol*K) * 100 K)
= (1,675,000 Pa*L) / (831.4 J/mol)
≈ 2016.6 mol
Therefore, there would be approximately 2016.6 moles of gas present if the gas followed ideal gas behavior.