Calculate the pressure and temperature at which 1.00 mole of CO gas will be in the same corresponding state as 1.00 mole of H2 gas at 2.00 bar and 30.0 degrees celsius. Use any critical constants necessary for both gases.
To calculate the pressure and temperature at which 1.00 mole of CO gas will be in the same corresponding state as 1.00 mole of H2 gas, we need to use the reduced variables and the corresponding states principle.
1. First, let's find the reduced variables for each gas:
- For CO gas, we need to use its critical constants: critical temperature (Tc) and critical pressure (Pc). The critical constants for CO gas are Tc = 132.9 °C (405.05 K) and Pc = 34.98 bar.
- For H2 gas, we will use its critical constants: Tc = -239.89 °C (33.26 K) and Pc = 12.97 bar.
2. Next, we'll calculate the reduced pressure (Pr) and reduced temperature (Tr) for each gas:
- For CO gas: Pr = P / Pc and Tr = T / Tc
- For H2 gas: Pr = P / Pc and Tr = T / Tc
3. We want to find the pressure and temperature at which both gases will be in the same corresponding state. This means their reduced variables will be equal, so we set up the following equation: PrCO = PrH2 and TrCO = TrH2.
4. Rearranging the equation, we have:
PCO / PcCO = PH2 / PcH2
TCO / TcCO = TH2 / TcH2
5. Now, let's substitute the given values into the equation:
PCO / 34.98 bar = 2.00 bar / 12.97 bar
TCO / 405.05 K = 30.0 °C / -239.89 °C
6. Solving for PCO, we find:
PCO = (2.00 bar / 12.97 bar) * 34.98 bar = 5.379 bar
7. Solving for TCO, we find:
TCO = (30.0 °C / -239.89 °C) * 405.05 K = -50.64 °C
Thus, the pressure and temperature at which 1.00 mole of CO gas will be in the same corresponding state as 1.00 mole of H2 gas are approximately 5.379 bar and -50.64 °C.