A mixture of 6.50 g He and 37.0 g Ne has a pressure of 610. mm Hg. What is the partial pressure of each of the gases?
To calculate the partial pressure of each gas in a mixture, we need to use Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.
First, we need to convert the given pressure from mm Hg to atm (atmospheres) since the most commonly used unit for pressure in gas calculations is atm.
1 atm = 760 mm Hg
So, 610 mm Hg is equal to 610/760 ≈ 0.80316 atm.
Next, we need to calculate the moles of each gas in the mixture. To do this, we'll use the ideal gas law:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Since the volume and temperature are not given, we assume that they are constant. Therefore, the equation can be rewritten as:
P1V1 = n1RT and P2V2 = n2RT
Since R and T are constant, we can ignore them for now.
We have two gases, He and Ne, so let's calculate the moles for each gas:
For He:
P1V1 = n1
n1 = P1V1 = (0.80316 atm) x V1
For Ne:
P2V2 = n2
n2 = P2V2 = (0.80316 atm) x V2
Now, we need to find the volumes. Since the pressure is given at constant temperature, we can ignore the volume and rewrite the equations in terms of moles:
n1 = 6.50 g He / molar mass of He
n2 = 37.0 g Ne / molar mass of Ne
The molar mass of helium (He) is approximately 4.00 g/mol, and the molar mass of neon (Ne) is approximately 20.18 g/mol.
n1 = 6.50 g He / 4.00 g/mol = 1.625 mol
n2 = 37.0 g Ne / 20.18 g/mol ≈ 1.835 mol
Now, we can calculate the partial pressure of each gas using the moles:
For He:
P1 = n1 x RT / V1 = (1.625 mol) x (0.0821 L·atm/mol·K) / V1
For Ne:
P2 = n2 x RT / V2 = (1.835 mol) x (0.0821 L·atm/mol·K) / V2
Since the total pressure of the mixture is 0.80316 atm, the sum of these two partial pressures must equal the total pressure:
P1 + P2 = 0.80316 atm
Given that, you can solve for the partial pressures of He and Ne by substituting the known values:
(1.625 mol) x (0.0821 L·atm/mol·K) / V1 + (1.835 mol) x (0.0821 L·atm/mol·K) / V2 = 0.80316 atm
This equation depends on the volumes of the gases, which are not given in the question. Therefore, to find the partial pressure of each gas, we need additional information about the volumes or a relationship between the volumes.