An ideal gas is sealed within a container at a tempreture of 17 degree celcies and a pressure of 101KPa. The container is heated until the tempreture of the gas reaches 100 degree celcies. A valve in the container is then opened to allow gas to escape until the pressure falls back to 101KPa at 100 degree celcies. 1) calculate the pressure in the gas just before the valve is opened. 2) calculate the fraction of the initial mass of gas that was lost as a result of opening the valve.
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1 a& b
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To solve these questions, we'll use the ideal gas law equation:
PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin.
1) To calculate the pressure in the gas just before the valve is opened:
Step 1: Convert the temperatures to Kelvin.
Initial temperature (T1) = 17°C + 273.15 = 290.15 K
Final temperature (T2) = 100°C + 273.15 = 373.15 K
Step 2: Use the ideal gas law equation to find the initial pressure (P1) and final pressure (P2).
P1V = nRT1
P2V = nRT2
Since the number of moles (n) and volume (V) are constant, we can equate the two equations:
P1T1 = P2T2
Rearrange the equation to solve for P1:
P1 = (P2T2) / T1
Substitute the given values:
P2 = 101 KPa
T2 = 373.15 K
T1 = 290.15 K
P1 = (101 KPa * 373.15 K) / 290.15 K
P1 ≈ 129.98 KPa
Therefore, the pressure in the gas just before the valve is opened is approximately 130 KPa.
2) To calculate the fraction of the initial mass of gas lost as a result of opening the valve, we'll assume that the gas behaves ideally and the container is rigid, so the volume remains constant.
Step 1: Use the ideal gas law to find the number of moles of gas initially (n1).
P1V = n1RT1
n1 = (P1V) / (RT1)
Since volume (V), pressure (P1), and temperature (T1) are constant, we can simplify the equation:
n1 = constant
Step 2: After opening the valve, the number of moles of gas remaining (n2) is given by:
P2V = n2RT2
n2 = (P2V) / (RT2)
Step 3: Calculate the fraction of the initial mass lost (lost_mass_fraction):
lost_mass_fraction = (n1 - n2) / n1
Since the masses of the gases are proportional to the number of moles, the fraction of the initial mass lost is the same as the fraction of the initial number of moles lost.
Substitute the given values:
P2 = 101 KPa
V = constant
T2 = 373.15 K
n2 = (101 KPa * V) / (RT2)
lost_mass_fraction = (n1 - n2) / n1
Note: For this step, you will need to know additional details about the system, such as the volume of the container or the number of moles initially. Without that information, it is not possible to calculate the exact fraction of the initial mass lost.
Overall, to solve these problems, we used the ideal gas law equation and made assumptions about the system being ideal and the volume being constant.