Final answer:
To calculate the total pressure inside the vessel containing nitrogen, hydrogen, and argon gases, convert the mass of each gas to moles, apply the ideal gas law to find the partial pressure of each gas, and then sum these partial pressures. Multiply by the appropriate conversion factor to express the pressure in torr.
Step-by-step explanation:
The question is asking to calculate the total pressure inside a vessel that contains nitrogen gas, hydrogen gas, and argon gas at a given temperature. In order to solve this, we can use the ideal gas law (PV = nRT) for each gas separately and add the individual pressures to get the total pressure because pressure is additive in a mixture of gases. Given: Volume (V) = 6.14 L, Temperature (T) = 277 K.
- First, convert the masses of the gases to moles using their molar masses (Nitrogen = 28.02 g/mol, Hydrogen = 2.02 g/mol, Argon = 39.95 g/mol).
- Calculate the moles of each gas: Moles of N2 = 1.82 g / 28.02 g/mol, Moles of H2 = 0.730 g / 2.02 g/mol, Moles of Ar = 59.0 g / 39.95 g/mol.
- Apply the ideal gas law for each gas to find its partial pressure.
- Add the partial pressures to find the total pressure inside the vessel.
- Convert the pressure to torr if necessary (1 atm = 760 torr).
Using the ideal gas constant R = 0.0821 L·atm/(mol·K), and rearranging the ideal gas equation to P = (nRT)/V, you can calculate the pressure contributed by each gas.