A 9.40-L container holds a mixture of two gases at 47 °C. The partial pressures of gas A and gas B, respectively, are 0.344 atm and 0.520 atm. If 0.160 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 need to consider the ideal gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

Given that the volume and temperature are constant (no change in volume or temperature), we can rearrange the ideal gas law equation to solve for pressure:

P = nRT / V

To find the total pressure, we need to calculate the total number of moles of gas in the container after the addition of the third gas.

The total number of moles can be calculated by adding the number of moles of each gas. Given that the partial pressure of gas A is 0.344 atm and the partial pressure of gas B is 0.520 atm, we can find the number of moles of each gas using the ideal gas law equation:

n = PV / RT

For gas A:
nA = (0.344 atm) * (9.40 L) / (0.0821 atm L/mol K) * (47 + 273.15) K

For gas B:
nB = (0.520 atm) * (9.40 L) / (0.0821 atm L/mol K) * (47 + 273.15) K

To find the total number of moles, we add nA, nB, and the number of moles of the third gas:

ntotal = nA + nB + 0.160 mol

Finally, to find the total pressure, we substitute the values into the formula:

Ptotal = (ntotal * R * T) / V

Substituting the known values into the equation, we can calculate the total pressure.

To find the total pressure after adding the third gas, we need to consider the partial pressure of the third gas and add it to the partial pressures of gas A and gas B.

First, let's calculate the moles of gas A and gas B in the container:

moles of gas A = partial pressure of gas A / total pressure * total moles
moles of gas A = 0.344 atm / total pressure * total moles

moles of gas B = partial pressure of gas B / total pressure * total moles
moles of gas B = 0.520 atm / total pressure * total moles

Now, let's find the total moles of gas in the container before adding the third gas:

total moles = moles of gas A + moles of gas B
total moles = (0.344 atm / total pressure * total moles) + (0.520 atm / total pressure * total moles)

To simplify the equation, let's abbreviate "total moles" as "T":

T = (0.344 atm / total pressure * T) + (0.520 atm / total pressure * T)

Next, we add the moles of the third gas:

new total moles = total moles + moles of third gas
new total moles = (0.344 atm / total pressure * T) + (0.520 atm / total pressure * T) + 0.160 mol

Since there is no change in volume or temperature, we can assume that the total volume and temperature remain constant.

Using the ideal gas law, PV = nRT, we can write:

(total pressure * total volume) = (total moles + moles of third gas) * (ideal gas constant * temperature)

Now we substitute the equation for new total moles:

(total pressure * total volume) = [(0.344 atm / total pressure * T) + (0.520 atm / total pressure * T) + 0.160 mol] * (ideal gas constant * temperature)

Simplifying the equation:

(total pressure * total volume) = [(0.344 atm * T) + (0.520 atm * T) + (0.160 mol * total pressure)] / total pressure

(total pressure * total volume) = [0.344 T + 0.520 T + 0.160 mol * total pressure] / total pressure

(total pressure * total volume) = (0.864 T + 0.160 mol * total pressure) / total pressure

Multiplying through by total pressure:

total pressure * total volume = 0.864 T + 0.160 mol * total pressure

Rearranging the equation:

total pressure * total volume - 0.160 mol * total pressure = 0.864 T

total pressure * (total volume - 0.160 mol) = 0.864 T

total pressure = (0.864 T) / (total volume - 0.160 mol)

Now we have an equation to find the total pressure after adding the third gas. Substitute the given values to calculate the total pressure.