1500 cm^3 of ideal gas at STP is cooled to -20°C and put into a 1000 cm^3 container. What is the final gauge pressure?
1-11 kPa
2-40 kPa
3-113 kPa
4-141 kPa
5-240 kPa
5
To find the final gauge pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = gas constant
T = temperature in Kelvin
Given:
Initial volume (V1) = 1500 cm^3
Final volume (V2) = 1000 cm^3
Initial temperature (T1) = Standard Temperature and Pressure (STP) = 0°C = 273.15 K
Final temperature (T2) = -20°C = 253.15 K
First, we need to calculate the initial pressure (P1) at STP using the ideal gas law:
P1 * V1 = n * R * T1
Since the gas is an ideal gas and at STP, we can assume the number of moles (n) and the gas constant (R) to be constant. Therefore, we can rewrite the equation as:
P1 = (n * R * T1) / V1
Next, we need to calculate the final pressure (P2) using the same equation, but with the final conditions:
P2 = (n * R * T2) / V2
Since both P1 and P2 have the same number of moles (n) and gas constant (R), we can compare the ratios of the pressures to find the final gauge pressure:
P2 / P1 = (n * R * T2 / V2) / (n * R * T1 / V1)
P2 / P1 = (T2 * V1) / (T1 * V2)
P2 = P1 * (T2 * V1) / (T1 * V2)
Now, let's plug in the values:
P1 = (n * R * T1) / V1 = (1 * 8.3145 J/(mol·K) * 273.15 K) / 1500 cm^3
P1 ≈ 0.478 kPa
P2 = 0.478 kPa * (253.15 K * 1500 cm^3) / (273.15 K * 1000 cm^3)
P2 ≈ 1.665 kPa
However, note that the given answer choices are in kPa and not the absolute pressure. Gauge pressure is the difference between absolute pressure and atmospheric pressure. Since the problem does not provide the atmospheric pressure, we cannot find the final gauge pressure without that information.
Therefore, the answer cannot be determined with the given information.