A 8.25-L container holds a mixture of two gases at 39 °C. The partial pressures of gas A and gas B, respectively, are 0.186 atm and 0.884 atm. If 0.120 mol of a third gas is added with no change in volume or temperature, what will the total pressure become?

To find the total pressure after adding the third gas, we can use Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas.

In this case, we already know the partial pressures of gas A (0.186 atm) and gas B (0.884 atm). We need to find out the partial pressure of the third gas.

First, let's determine the moles of the third gas. We are given that 0.120 mol of the third gas is added.

Next, we know that the volume (V) and temperature (T) remain constant. Therefore, according to Charles's law, the total pressure is directly proportional to the number of moles of gas.

Now, let's calculate the partial pressure of the third gas:

Partial pressure of third gas = moles of third gas/total moles of gas x total pressure

Total moles of gas = moles of gas A + moles of gas B + moles of third gas

Since we have the moles of the third gas (0.120 mol) and the moles of gas A and gas B are not given directly, we need to calculate them.

To determine the moles of gas A and gas B, we will use the ideal gas law:

PV = nRT

Rearranging the equation, we have:

n = PV/RT

For gas A:
nA = (0.186 atm)(8.25 L)/(0.0821 atm·L/mol·K)(312 K)
= 0.750 mol

For gas B:
nB = (0.884 atm)(8.25 L)/(0.0821 atm·L/mol·K)(312 K)
= 3.550 mol

Now that we have the moles of gas A (0.750 mol) and gas B (3.550 mol), we can calculate the total moles of gas:

Total moles of gas = 0.750 mol + 3.550 mol + 0.120 mol
= 4.420 mol

Now, we can calculate the partial pressure of the third gas:

Partial pressure of third gas = (0.120 mol/4.420 mol)(Total pressure)

Finally, we can calculate the total pressure:

Total pressure = partial pressure of gas A + partial pressure of gas B + partial pressure of third gas