A compressed gas in a cylinder contains 1000.0 g of argon gas.
The pressure inside the cylinder is 2050 psi at 18 degrees Celcius. How much gas remains if the pressure is decreased to 650. psi at a temperature of 26 degrees Celcius?
The problem says nothing about opening a valve so you have the same amount of gas you started with unless there's a leak somewhere.
To calculate the amount of gas remaining, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
To find the amount of gas remaining, we need to compare the initial conditions to the final conditions while keeping the number of moles constant.
Step 1: Convert the initial and final pressures to standard units:
Initial pressure = 2050 psi
Final pressure = 650 psi
Since we need to convert the pressure to standard units (usually in pascals), we'll use the conversion factor: 1 psi = 6894.76 Pascals.
Initial pressure in Pascals = 2050 psi * 6894.76 Pa/psi
Final pressure in Pascals = 650 psi * 6894.76 Pa/psi
Step 2: Convert the temperatures to Kelvin:
Initial temperature = 18 degrees Celsius
Final temperature = 26 degrees Celsius
To convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature.
Initial temperature in Kelvin = 18 degrees Celsius + 273.15
Final temperature in Kelvin = 26 degrees Celsius + 273.15
Step 3: Calculate the number of moles using the ideal gas law equation:
To compare the initial and final conditions, we can set up the equation:
(P1 * V1) / (n1 * R * T1) = (P2 * V2) / (n2 * R * T2)
Since we want to find the final number of moles (n2), we'll rearrange the equation as follows:
n2 = (P2 * V2 * n1 * R * T1) / (P1 * V1 * R * T2)
However, since we want to determine the amount of gas remaining, we can assume the volume (V) remains constant. So we can simplify the equation further:
n2 = (P2 * n1 * T1) / (P1 * T2)
Step 4: Calculate the number of moles of argon gas remaining:
Substitute the given values into the equation:
n2 = (650 psi * n1 * (18 degrees Celsius + 273.15)) / (2050 psi * (26 degrees Celsius + 273.15))
Step 5: Calculate the mass of gas remaining:
To find the mass of the gas remaining, we need to multiply the number of moles by the molar mass of argon, which is approximately 39.95 g/mol.
Mass of gas remaining = n2 * molar mass of argon
Finally, plug the calculated values into the equation to find the mass of gas remaining.