To a tank already containing N2 at 2.0 atm and O2 at 1.0 atm, we add an unknown quantity of CO2 until the total pressure is 4.6 atm. What is the partial pressure of the CO2?
To find the partial pressure of CO2, we can use Dalton's law of partial pressures.
According to Dalton's law, the total pressure (Pt) is the sum of the partial pressures of each gas in the mixture.
Given:
Partial pressure of N2 (Pn2) = 2.0 atm
Partial pressure of O2 (Po2) = 1.0 atm
Total pressure (Pt) = 4.6 atm
We need to find the partial pressure of CO2 (Pco2).
Using Dalton's law, we can write the equation:
Pt = Pn2 + Po2 + Pco2
Substituting the given values:
4.6 atm = 2.0 atm + 1.0 atm + Pco2
Now, let's solve for Pco2:
Pco2 = 4.6 atm - (2.0 atm + 1.0 atm)
Pco2 = 4.6 atm - 3.0 atm
Pco2 = 1.6 atm
Therefore, the partial pressure of CO2 in the tank is 1.6 atm.
To find the partial pressure of CO2 in the tank, we first need to understand the concept of partial pressure.
Partial pressure is the pressure exerted by an individual gas component in a mixture of gases. It is calculated by multiplying the mole fraction of the gas by the total pressure of the mixture.
In this case, we have three gases in the tank: N2, O2, and CO2.
Let's start by calculating the mole fractions of N2 and O2:
Mole fraction (N2) = moles of N2 / total moles of gas
Mole fraction (O2) = moles of O2 / total moles of gas
Since we don't know the quantity of CO2 added, we do not have its moles. However, since the total pressure is given, we can use Dalton's law of partial pressures to find the partial pressure of CO2.
According to Dalton's law of partial pressures, the total pressure of a gas mixture is equal to the sum of the partial pressures of each individual gas.
Therefore, the partial pressure of CO2 can be calculated as follows:
Partial pressure (CO2) = Total pressure - (Partial pressure (N2) + Partial pressure (O2))
To calculate the partial pressures of N2 and O2, we use the mole fractions:
Partial pressure (N2) = Mole fraction (N2) * Total pressure
Partial pressure (O2) = Mole fraction (O2) * Total pressure
Let's substitute the given values:
Mole fraction (N2) = (moles of N2) / (moles of N2 + moles of O2 + moles of CO2)
Mole fraction (O2) = (moles of O2) / (moles of N2 + moles of O2 + moles of CO2)
Mole fraction (N2) = (2.0 atm) / (2.0 atm + 1.0 atm + moles of CO2)
Mole fraction (O2) = (1.0 atm) / (2.0 atm + 1.0 atm + moles of CO2)
Next, we calculate the partial pressures:
Partial pressure (N2) = Mole fraction (N2) * Total pressure
Partial pressure (O2) = Mole fraction (O2) * Total pressure
Partial pressure (CO2) = Total pressure - (Partial pressure (N2) + Partial pressure (O2))
Given that the total pressure is 4.6 atm, we can substitute this value:
Partial pressure (N2) = (2.0 atm) / (2.0 atm + 1.0 atm + moles of CO2) * 4.6 atm
Partial pressure (O2) = (1.0 atm) / (2.0 atm + 1.0 atm + moles of CO2) * 4.6 atm
Partial pressure (CO2) = 4.6 atm - (Partial pressure (N2) + Partial pressure (O2))
To find the partial pressure of CO2, you would need to know the moles of N2 and O2 or more information about the gases in the tank. Without that information, it is not possible to calculate the partial pressure of CO2.