Answer:
we can use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
First, we can find the total number of moles of gas in the container:
n(total) = n(A) + n(B)
To find the number of moles of each gas, we can use the partial pressures and the total pressure:
P(A) / P(total) = n(A) / n(total)
P(B) / P(total) = n(B) / n(total)
We can rearrange these equations to solve for n(A) and n(B):
n(A) = P(A) / P(total) × n(total)
n(B) = P(B) / P(total) × n(total)
We know that the partial pressures of gas A and gas B are 0.264 atm and 0.548 atm, respectively, and we can find the total pressure by adding these partial pressures:
P(total) = P(A) + P(B) = 0.264 atm + 0.548 atm = 0.812 atm
We can also find the total number of moles of gas in the container:
n(total) = PV / RT = (0.812 atm) × (9.10 L) / (0.08206 L·atm/mol·K × 316 K) = 0.286 mol
Now we can add 0.130 mol of a third gas, which gives us a new total number of moles of gas:
n(new) = n(total) + 0.130 mol = 0.286 mol + 0.130 mol = 0.416 mol
Since there is no change in volume or temperature, the new total pressure will be proportional to the total number of moles of gas:
P(new) = P(total) × n(new) / n(total) = (0.812 atm) × (0.416 mol) / (0.286 mol) = 1.18 atm
Therefore, the total pressure will become 1.18 atm.