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. How do I approach this question?
To approach this question, we can use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas. The ideal gas law equation is given as: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
First, we need to find the values for 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.
Step 1: Convert the temperature from Celsius to Kelvin.
Since the ideal gas law requires temperature in Kelvin, we need to convert the given temperature from Celsius to Kelvin by adding 273.15:
T (in Kelvin) = 30.0°C + 273.15 = 303.15K
Step 2: Plug in the given values of H2 gas into the ideal gas law equation.
P (H2) = 2.00 bar = 2.00 x 10^5 Pa (since 1 bar = 10^5 Pa)
n (H2) = 1.00 mole
R = 8.314 J/(mol K) (universal gas constant)
Step 3: Rearrange the ideal gas law equation to solve for the unknown, which is the pressure and temperature of CO gas.
P (CO) = (n (CO) x R x T (CO)) / V (CO)
Since the volumes are not given and we are comparing the two gases in the same state, we can assume the volumes to be equal. Therefore, the ratio of the number of moles will be equal to the ratio of pressures and temperatures.
Step 4: Calculate the pressure and temperature of CO gas.
Using the ratio of moles, we have:
P (CO) / P (H2) = n (CO) / n (H2)
P (CO) / 2.00 x 10^5 Pa = 1.00 mole / 1.00 mole
P (CO) = 2.00 x 10^5 Pa
Next, for temperature:
T (CO) / T (H2) = n (CO) / n (H2)
T (CO) / 303.15K = 1.00 mole / 1.00 mole
T (CO) = 303.15K
Therefore, at 2.00 bar and 30.0 degrees Celsius, 1.00 mole of CO gas will be in the same corresponding state as 1.00 mole of H2 gas at a pressure of 2.00 x 10^5 Pa and a temperature of 303.15K.