A sample containing 7.20g O2 gas has a volume of 33.0L Pressure and temperature remain constant. What is the volume after 4.00g He is added to the O2 gas already in the container?
To find the volume after adding helium gas to the existing oxygen gas, we will use the concept of the combined gas law. The combined gas law states that the ratio of the initial volume of gas to the final volume of gas is equal to the ratio of the initial moles of gas to the final moles of gas, given that the pressure and temperature remain constant.
Here's how we can solve it step by step:
Step 1: Determine the moles of oxygen gas (O2).
We can calculate the moles of O2 using its molar mass.
Molar mass of O2 = 32.00 g/mol
Moles of O2 = Mass of O2 / Molar mass of O2
= 7.20 g / 32.00 g/mol
= 0.225 mol
Step 2: Calculate the final volume.
We can use the combined gas law formula to calculate the final volume of the gas.
(V1 / V2) = (n1 / n2)
Where:
V1 = Initial volume of the gas (given: 33.0 L)
V2 = Final volume of the gas (to be calculated)
n1 = Initial moles of the gas (calculated: 0.225 mol)
n2 = Final moles of the gas (to be calculated)
(V1 / V2) = (n1 / n2)
33.0 L / V2 = 0.225 mol / (0.225 mol + n2)
(33.0 L / V2) = 0.225 mol / (0.225 mol + n2)
Step 3: Calculate the moles of helium gas (He).
Since helium (He) is being added, we need to determine its moles.
Molar mass of He = 4.00 g/mol
Moles of He = Mass of He / Molar mass of He
= 4.00 g / 4.00 g/mol
= 1.00 mol
Step 4: Solve for n2.
We can substitute the values for n1, n2, and the moles of He into the equation we derived in Step 2.
(33.0 L / V2) = 0.225 mol / (0.225 mol + 1.00 mol)
Step 5: Solve for V2.
Rearrange the formula to solve for V2:
V2 = (0.225 mol + 1.00 mol) / (33.0 L / V2)
Cross multiply:
V2 * (0.225 mol + 1.00 mol) = 33.0 L
Combine the moles:
V2 * 1.225 mol = 33.0 L
Divide both sides by 1.225 mol:
V2 = 33.0 L / 1.225 mol
V2 ≈ 26.94 L
Therefore, the volume after adding 4.00g of helium gas to the existing oxygen gas is approximately 26.94 L.
7.2 gO2/32 g/mol = 0.225 moles O2.
I would use PV = nRT and solve for P, then add 4/4 = 1.0 mole He to make a total of 1.225 mol combined gases and plug into PV = nRT again and solve for V.
You also can use a ratio/proportion.
(33/0.225) = (V/1.225) and solve for V.