Final answer:
To find the total pressure of the gas mixture, we can use the ideal gas law equation and calculate the number of moles of each gas. Then, we can substitute these values into the equation to find the total pressure.
Step-by-step explanation:
To find the total pressure of the gas mixture, we can use the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
In this case, we have the volume (30.0 L) and the temperature (in degree Celsius). We also have the masses of the two gases (80.0 g of Ar and 142 g of oxygen). To find the number of moles of each gas, we can use the formula:
n = m/M
Where n is the number of moles, m is the mass, and M is the molar mass of the gas.
We can then calculate the total number of moles and substitute it into the ideal gas law equation to find the total pressure of the gas mixture.
Let's start by calculating the number of moles of Ar:
n(Ar) = 80.0 g / (39.95 g/mol) = 2.00 mol
Next, let's calculate the number of moles of oxygen:
n(O₂) = 142 g / (32.00 g/mol) = 4.44 mol
The total number of moles is:
n(total) = n(Ar) + n(O₂) = 2.00 mol + 4.44 mol = 6.44 mol
Now, we can substitute the values into the ideal gas law equation:
P(30.0 L) = (6.44 mol) (0.0821 L·atm/mol·K) (T in Kelvin)
Since the temperature is given in degrees Celsius, we need to convert it to Kelvin by adding 273.15:
T(K) = T(°C) + 273.15
Once we have the value of T in Kelvin, we can rearrange the equation to solve for P:
P(total) = (6.44 mol) (0.0821 L·atm/mol·K) (T in Kelvin) / (30.0 L)
Now, we can calculate the value of the total pressure using the given temperature in degree Celsius.