a process stream containing acetone vapour in nitrogen enters a cooler compressor at 65 degree celcius and 1 atm, with relative saturation of acetone equal to 50%. the gas is compressed and cooled to 20 degree celcius to recover 95% of acetone as a liquid. calculate the outlet pressure and the ratio
To calculate the outlet pressure and the ratio, we can use the ideal gas law and the Antoine equation to determine the properties of acetone vapor at different temperatures.
1. Determine the saturation pressure of acetone vapor at 65 °C:
- The Antoine equation for acetone is: log(P) = A - (B / (T + C))
- For acetone, the Antoine coefficients are:
A = 14.3142, B = 2756.22, and C = -46.13 (in °C and mmHg units)
- Convert the temperature to Kelvin (K): T = 65 + 273.15 = 338.15 K
- Using the Antoine equation, calculate the saturation pressure of acetone at 65 °C.
2. Calculate the actual partial pressure of acetone:
- The relative saturation of acetone at the inlet is 50%, which means the partial pressure of acetone is 0.5 times the saturation pressure at 65 °C.
3. Calculate the partial pressure of nitrogen:
- Since nitrogen is an ideal gas, it follows Dalton's law of partial pressure. The partial pressure of nitrogen can be calculated by subtracting the partial pressure of acetone from the total pressure, which is 1 atm.
4. Apply the ideal gas law to calculate the outlet pressure:
- Use the ideal gas law equation: PV = nRT
- n = number of moles of gas, R = ideal gas constant, T = temperature in Kelvin
- Use the known values: P = total pressure (1 atm), V = volume, n = number of moles (which remains constant in this process), R = ideal gas constant, T = temperature in Kelvin (20 °C = 293.15 K)
- Rearrange the equation to solve for outlet pressure (P_out) when volume (V) is also given.
5. Calculate the ratio:
- The ratio refers to the volume of the acetone liquid recovered compared to the initial volume of the acetone vapor. Since 95% of the acetone is recovered as a liquid, the ratio is 0.95.
By following these steps and plugging in the given values, you can calculate the outlet pressure and the ratio.