Two flask were connected by a narrow glass tube with a closed tap. One flask contained 300cm^3 of oxygen at 1.0x10^5Nm^-2 while the 200cm^3 of notrogen at 2.0x10^5Nm^-2.After opening the tap, calculate the
(a)partial pressure of each gas.
(b)total pressure of the mixture at constant temperature.?
PV = nRT. Since R is constant and T is constant, then PV = nk and since T doesn't change then k stays the same so for this problem we can write PV = n (basically we are calling k = 1) and n = PV.
1st flask = n = 1E5*0.3 = 0.3E5
2nd flask = n = 2E5*0.2 = 0.4E5
Total n = 0.7E5
Total P = n/V = 0.7E5/0.5 = ? N/m^2
partial pressure of each is n/V = ?
Post your work if you get stuck.
To solve this problem, we can use the principles of Dalton's Law of Partial Pressures. According to this law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.
(a) To calculate the partial pressure of each gas, we can use the formula:
Partial pressure of a gas = (Total pressure) x (Volume of the gas) / (Total volume)
Given:
Oxygen volume (V1) = 300 cm^3
Oxygen pressure (P1) = 1.0 x 10^5 Nm^-2
Nitrogen volume (V2) = 200 cm^3
Nitrogen pressure (P2) = 2.0 x 10^5 Nm^-2
First, let's calculate the total pressure (P) of the mixture. Since the tap is closed, the total volume of the gases remains the sum of the two volumes.
Total volume (V) = V1 + V2 = 300 cm^3 + 200 cm^3 = 500 cm^3
Now we can calculate the partial pressure of oxygen (PO2):
PO2 = P1 x V1 / V = (1.0 x 10^5 Nm^-2) x (300 cm^3) / (500 cm^3)
PO2 = 60000 Nm^-2
Next, we can calculate the partial pressure of nitrogen (PN2):
PN2 = P2 x V2 / V = (2.0 x 10^5 Nm^-2) x (200 cm^3) / (500 cm^3)
PN2 = 80000 Nm^-2
Therefore, the partial pressure of oxygen (PO2) is 60000 Nm^-2 and the partial pressure of nitrogen (PN2) is 80000 Nm^-2.
(b) To calculate the total pressure (PT) of the mixture, we simply add the partial pressures of each gas:
PT = PO2 + PN2
PT = 60000 Nm^-2 + 80000 Nm^-2
PT = 140000 Nm^-2
Therefore, the total pressure of the mixture is 140000 Nm^-2.
To calculate the partial pressure of each gas and the total pressure of the mixture, we can use the ideal gas law. The ideal gas law states:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
To calculate the partial pressure of each gas, we can 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 gas. Mathematically, this can be written as:
P_total = P_1 + P_2
Now, let's calculate the partial pressure of each gas and the total pressure of the mixture:
(a) Partial Pressure of each gas:
From the given information, we have:
For oxygen:
Volume (V_oxygen) = 300 cm³
Pressure (P_oxygen) = 1.0x10^5 Nm^-2
For nitrogen:
Volume (V_nitrogen) = 200 cm³
Pressure (P_nitrogen) = 2.0x10^5 Nm^-2
To calculate the partial pressure of each gas, we need to convert the volumes to the same units, preferably m³. Since 1 m³ is equal to 1000000 cm³:
V_oxygen = 300 cm³ = 300/1000000 m³ = 0.0003 m³
V_nitrogen = 200 cm³ = 200/1000000 m³ = 0.0002 m³
Now we convert the volumes to moles using the ideal gas law. Assuming the temperature is constant, we can use the formula:
n = PV / RT
Using the value of R = 8.314 J/(mol·K) and a constant temperature, we can calculate the moles of oxygen and nitrogen:
For oxygen:
n_oxygen = (P_oxygen * V_oxygen) / (R * T)
For nitrogen:
n_nitrogen = (P_nitrogen * V_nitrogen) / (R * T)
Once we have the moles of each gas, we can calculate the partial pressure of each gas using:
P_partial = n_gas * R * T / V_gas
(b) Total pressure of the mixture:
The total pressure of the mixture is the sum of the partial pressures of each gas:
P_total = P_oxygen + P_nitrogen
With these calculations, we can determine the partial pressure of each gas and the total pressure of the mixture.