A mixture of gases contains 0.4 mole of N2, 0.5 moles of O2, and 0.7 moles of H2. What is the total
pressure if partial pressure of O2 is 1.3 atm?
Determine mole fraction, X, of O2.
XO2 = mols O2/total mols.
Then XO2*Ptotal = PO2.
Solve for Ptotal.
Well, it seems like we have a mixture of gases enjoying their little gas party! Let's figure out the total pressure, shall we?
First, we need to calculate the partial pressure of each gas. We know that the partial pressure of O2 is 1.3 atm.
Now, we can use the mole ratios to find the partial pressure of N2 and H2. Since we have 0.5 moles of O2 and 0.4 moles of N2, the mole ratio of O2 to N2 is 0.5:0.4, which simplifies to 1.25:1.
So, if the partial pressure of O2 is 1.3 atm, the partial pressure of N2 would be 1.3 atm * (1/1.25) = 1.04 atm.
Similarly, if we have 0.7 moles of H2, the mole ratio of O2 to H2 is 0.5:0.7, which simplifies to 5:7. So, the partial pressure of H2 would be 1.3 atm * (5/7) = 0.93 atm.
Now we can add up all the partial pressures to get the total pressure:
Total pressure = Partial pressure of N2 + Partial pressure of O2 + Partial pressure of H2
= 1.04 atm + 1.3 atm + 0.93 atm
= 3.27 atm
So, my friend, the total pressure of the gas mixture is 3.27 atmospheres. Keep those gases partying responsibly! 🎉🔥
To find the total pressure of the mixture of gases, we can use Dalton's Law of Partial Pressures. According to Dalton's law, the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each gas component.
Given:
Mole of N2 (nN2) = 0.4 moles
Mole of O2 (nO2) = 0.5 moles
Mole of H2 (nH2) = 0.7 moles
Partial pressure of O2 (PO2) = 1.3 atm
Step 1: Calculate the mole fraction for each gas component.
Mole fraction (Xi) of a component i is given by the equation:
Xi = ni / ntotal
where ni is the number of moles of the component i and ntotal is the total number of moles of all the gas components.
For N2:
XN2 = nN2 / (nN2 + nO2 + nH2)
For O2:
XO2 = nO2 / (nN2 + nO2 + nH2)
For H2:
XH2 = nH2 / (nN2 + nO2 + nH2)
Step 2: Calculate the partial pressure of each gas component.
The partial pressure (Pi) of a component i is given by the equation:
Pi = Xi * Ptotal
where Xi is the mole fraction of the component i and Ptotal is the total pressure.
For N2:
PN2 = XN2 * Ptotal
For O2:
PO2 = XO2 * Ptotal
For H2:
PH2 = XH2 * Ptotal
Step 3: Determine the total pressure.
Since we are given that the partial pressure of O2 is 1.3 atm, we can substitute the values into the equation and solve for Ptotal.
PO2 = XO2 * Ptotal
1.3 atm = XO2 * Ptotal
Substituting the mole fraction of O2:
1.3 atm = (0.5 moles / (0.4 moles + 0.5 moles + 0.7 moles)) * Ptotal
Simplifying the equation:
1.3 atm = (0.5 moles / 1.6 moles) * Ptotal
Solving for Ptotal:
Ptotal = 1.3 atm * (1.6 moles / 0.5 moles)
Ptotal = 4.16 atm
Therefore, the total pressure of the mixture of gases is 4.16 atm.
To calculate the total pressure of the mixture of gases, we can use Dalton's law, which states that the total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas.
Given that the partial pressure of O2 is 1.3 atm, we can use this information to calculate the partial pressures of each gas in the mixture:
Partial pressure of N2 = (moles of N2 / total moles of gas) * total pressure
Partial pressure of O2 = (moles of O2 / total moles of gas) * total pressure
Partial pressure of H2 = (moles of H2 / total moles of gas) * total pressure
Let's calculate the partial pressure of each gas using the given information:
Partial pressure of N2 = (0.4 moles / (0.4 moles + 0.5 moles + 0.7 moles)) * total pressure
Partial pressure of O2 = (0.5 moles / (0.4 moles + 0.5 moles + 0.7 moles)) * 1.3 atm
Partial pressure of H2 = (0.7 moles / (0.4 moles + 0.5 moles + 0.7 moles)) * total pressure
Now, we can solve this system of equations to find the total pressure.
0.4 / (0.4 + 0.5 + 0.7) * total pressure + 0.5 / (0.4 + 0.5 + 0.7) * 1.3 atm + 0.7 / (0.4 + 0.5 + 0.7) * total pressure = total pressure
Simplifying the equation:
0.4 / 1.6 * total pressure + 0.5 / 1.6 * 1.3 atm + 0.7 / 1.6 * total pressure = total pressure
0.25 * total pressure + 0.40625 atm + 0.4375 * total pressure = total pressure
Combining like terms:
0.6875 * total pressure + 0.40625 atm = total pressure
Rearranging the equation to solve for the total pressure:
0.6875 * total pressure - total pressure = -0.40625 atm
(0.6875 - 1) * total pressure = -0.40625 atm
-0.3125 * total pressure = -0.40625 atm
Dividing both sides by -0.3125:
total pressure = -0.40625 atm / -0.3125
total pressure = 1.3 atm
Therefore, the total pressure of the mixture of gases is 1.3 atm.