Final answer:
The total pressure of the mixture of gases is 4.86 atm, and the partial pressure of Ar is approximately 1.08 atm.
Step-by-step explanation:
To find the total pressure of the mixture of gases, we can use Dalton's law of partial pressure. According to this law, the total pressure is equal to the sum of the partial pressures of each gas in the mixture. In this case, we have 7.0 moles of He and 2.0 moles of Ar in an 8L container at 450K.
To calculate the partial pressure of Ar, we can use the formula:
Partial Pressure (PAr) = (moles of Ar / total moles of gas) x Total Pressure
In this case, the total moles of gas is 9.0 moles (7.0 moles of He + 2.0 moles of Ar). Therefore, the partial pressure of Ar is:
PAr = (2.0 moles / 9.0 moles) x Total Pressure
To find the total pressure, we need to use the ideal gas law:
Pressure x Volume = nRT
Where n is the total number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. Rearranging the equation gives us:
Pressure = (nRT) / Volume
Substituting the values into the equation, we can calculate the total pressure:
Total Pressure = (9.0 moles x 0.0821 atm/mol·K x 450K) / 8L
So, the total pressure of the mixture of gases is 4.86 atm. To find the partial pressure of Ar, we can substitute the values into the formula:
PAr = (2.0 moles / 9.0 moles) x 4.86 atm
Therefore, the partial pressure of Ar is approximately 1.08 atm.