Calculate the partial pressure of 4.0 g methane when mixed with 16.0 g oxygen. The total pressure of both gases is 600. torr.
To calculate the partial pressure of methane in the mixture, we need to determine the mole fraction of methane and then use it to find its partial pressure.
Step 1: Calculate the moles of methane and oxygen.
Moles of methane (CH4) = mass / molar mass
Molar mass of methane = 12.01 g/mol (C) + 4(1.01 g/mol) (H) = 16.05 g/mol
Moles of methane = 4.0 g / 16.05 g/mol = 0.249 mol
Moles of oxygen (O2) = mass / molar mass
Molar mass of oxygen = 2(16.00 g/mol) = 32.00 g/mol
Moles of oxygen = 16.0 g / 32.00 g/mol = 0.500 mol
Step 2: Calculate the total moles of both gases.
Total moles of gas = moles of methane + moles of oxygen
Total moles of gas = 0.249 mol + 0.500 mol = 0.749 mol
Step 3: Calculate the mole fraction of methane.
Mole fraction of methane = moles of methane / total moles of gas
Mole fraction of methane = 0.249 mol / 0.749 mol = 0.332
Step 4: Calculate the partial pressure of methane.
Partial pressure of methane = mole fraction of methane x total pressure
Partial pressure of methane = 0.332 x 600 torr = 199.2 torr
Therefore, the partial pressure of 4.0 g methane, when mixed with 16.0 g oxygen and a total pressure of 600 torr, is 199.2 torr.
To calculate the partial pressure of a gas, we need to use the concept of the mole fraction. The mole fraction of a gas is the ratio of the number of moles of that gas to the total number of moles in the mixture.
Let's first calculate the number of moles of methane and oxygen. We will use the molar mass of each gas to convert the given masses to moles.
The molar mass of methane (CH4) is calculated as follows:
1 atom of C (carbon) × 12.01 g/mol = 12.01 g/mol
4 atoms of H (hydrogen) × 1.01 g/mol = 4.04 g/mol
Total molar mass of methane = 12.01 g/mol + 4.04 g/mol = 16.05 g/mol
Number of moles of methane = 4.0 g ÷ 16.05 g/mol = 0.249 moles
The molar mass of oxygen (O2) is calculated as follows:
2 atoms of O (oxygen) × 16.00 g/mol = 32.00 g/mol
Number of moles of oxygen = 16.0 g ÷ 32.00 g/mol = 0.500 moles
Now let's calculate the mole fraction of methane and oxygen:
Mole fraction of methane = moles of methane ÷ total moles in the mixture
Mole fraction of methane = 0.249 moles ÷ (0.249 moles + 0.500 moles) = 0.332
Since the total pressure of both gases is given as 600 torr, we can use the mole fraction of methane to calculate its partial pressure.
Partial pressure of methane = mole fraction of methane × total pressure
Partial pressure of methane = 0.332 × 600 torr = 199.2 torr
Therefore, the partial pressure of 4.0 g of methane when mixed with 16.0 g of oxygen is 199.2 torr.