A 8.90-L container holds a mixture of two gases at 45 C. The partial pressures of gas A and gas B, respectively, are .294 atm and .860 atm. If .100 mol of a third gas is added with no change in volume or temperature, what will the total pressure become?
You can do this the long way.
PV = nRT
You know P, V, solve for n, you know R and T. I would add the two partial pressures for A and B and solve for n, then add 0.100 mole to that and recalculate P.
To find the total pressure after adding the third gas, we need to consider Dalton's law of partial pressures. According to Dalton's law, the total pressure of a mixture of gases is equal to the sum of the partial pressures of each gas.
In this case, the initial mixture consists of two gases: gas A and gas B. The partial pressures of gas A and gas B are given as 0.294 atm and 0.860 atm, respectively.
To find the total pressure after adding the third gas, we need to calculate what the partial pressure of the third gas will be. Since the volume and the temperature remain constant, we can assume that the moles of gas A and gas B do not change.
Given that 0.100 mol of the third gas is added, we can calculate its partial pressure by subtracting the initial partial pressures of gas A and gas B from the total pressure:
Partial pressure of the third gas = Total pressure - Partial pressure of gas A - Partial pressure of gas B
Using this formula, we can find the partial pressure of the third gas.
Total pressure = Partial pressure of gas A + Partial pressure of gas B + Partial pressure of the third gas
Total pressure = 0.294 atm + 0.860 atm + Partial pressure of the third gas
Now, we have two values of partial pressures and need to find the third one. Let's substitute the known values:
Total pressure = 0.294 atm + 0.860 atm + Partial pressure of the third gas
To find the partial pressure of the third gas, we need to rearrange the equation:
Partial pressure of the third gas = Total pressure - (Partial pressure of gas A + Partial pressure of gas B)
Partial pressure of the third gas = 0.294 atm + 0.860 atm + Partial pressure of the third gas
Partial pressure of the third gas = 1.154 atm
Therefore, the total pressure after adding the third gas will be 1.154 atm.