A 1.00-L gas sample at 100°C and 600 torr contains 50% helium and 50% xenon by mass. What are the partial pressures of the individual gas?

partial pressure for He: 582 torr & 18 torr for xe

Pick any convenient number for the total mass, then half of that is He and half is Xe.

Now find the moles.
moles = grams/molar mass.

Calculate mole fraction He and mole fraction Xe.
mole fraction He = mol He/total moles and
mole fraction Xe = mol Xe/total moles.

Finally,
PHe = mole fraction He*total P (which is 600 torr).
PXe = mole fraction Xe*total P.

To find the partial pressures of each gas in the mixture, we need to use the ideal gas law and Dalton's law of partial pressures.

1. Start by calculating the moles of each gas in the mixture.
- Given that the gas sample is 1.00 L, we can assume that the amounts of gases are also in liters.
- Since the gas sample contains 50% helium and 50% xenon by mass, the moles of helium in the mixture will be equal to the moles of xenon.
- To calculate the moles of helium, we need to know the molar mass of helium and the mass of helium in the mixture.
- The molar mass of helium (He) is approximately 4 g/mol.
- We can assume a total mass of 100 g for the mixture.
- Therefore, the mass of helium in the mixture is 50 g.
- Now, we can calculate the moles of helium.
- Moles of helium = mass of helium / molar mass of helium
= 50 g / 4 g/mol
= 12.5 mol

2. Since the moles of helium and xenon are equal, the moles of xenon are also 12.5 mol.

3. Next, we need to calculate the partial pressures of each gas using Dalton's law of partial pressures.
- Dalton's law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
- The partial pressure of each gas is equal to its mole fraction multiplied by the total pressure of the mixture.
- Mole fraction of helium = moles of helium / total moles of both gases
= 12.5 mol / (12.5 mol + 12.5 mol)
= 0.5
- Mole fraction of xenon = moles of xenon / total moles of both gases
= 12.5 mol / (12.5 mol + 12.5 mol)
= 0.5
- Total pressure of the mixture = 600 torr

- Now, we can calculate the partial pressures of each gas.
- Partial pressure of helium = mole fraction of helium * total pressure of the mixture
= 0.5 * 600 torr
= 300 torr
- Partial pressure of xenon = mole fraction of xenon * total pressure of the mixture
= 0.5 * 600 torr
= 300 torr

4. The partial pressures of helium and xenon in the gas sample are 300 torr each.

To calculate the partial pressures of the individual gases, we can use the Dalton's Law of Partial Pressures.

According to Dalton's Law of Partial Pressures, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas in the mixture.

Given:
Total volume (V) = 1.00 L
Temperature (T) = 100°C = 373 K
Total pressure (P_total) = 600 torr
Mass percent of helium (φ_he) = 50%
Mass percent of xenon (φ_xe) = 50%

We need to find the partial pressures of helium (P_he) and xenon (P_xe).

First, let's find the moles of each gas:
1. Calculate the moles of helium (n_he):
Molar mass of helium (M_he) = 4.0026 g/mol
n_he = (φ_he * mass) / M_he
= (0.50 * mass) / M_he

2. Calculate the moles of xenon (n_xe):
Molar mass of xenon (M_xe) = 131.293 g/mol
n_xe = (φ_xe * mass) / M_xe
= (0.50 * mass) / M_xe

Next, let's find the partial pressure of each gas using the ideal gas law:

1. Calculate the partial pressure of helium (P_he):
P_he = (n_he * R * T) / V

2. Calculate the partial pressure of xenon (P_xe):
P_xe = (n_xe * R * T) / V

Where:
R is the ideal gas constant, which is 0.0821 L·atm/(mol·K)

Now, let's substitute the values and calculate the partial pressures.