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.