A 9.00-L container holds a mixture of two gases at 43 °C. The partial pressures of gas A and gas B, respectively, are 0.257 atm and 0.579 atm. If 0.110 mol a third gas is added with no change in volume or temperature, what will the total pressure become?
Use PV = nRT and calculate the partial pressure of the third gas, than add the partial pressure of the three to obtain the total.
To find the total pressure after adding the third gas, we can use Dalton's Law of Partial Pressures. According to Dalton's Law, the total pressure exerted by a mixture of gases is equal to the sum of the individual pressures of each gas.
The partial pressures of gas A and B are given as 0.257 atm and 0.579 atm, respectively. To find the total pressure after adding the third gas, we need to calculate the partial pressure of the third gas.
Since the volume and temperature remain constant, we can assume that the number of moles of the total gas remains the same after adding the third gas. Therefore, we can consider the initial number of moles (0.110 mol) and the newly added gas as a single gas mixture.
To find the partial pressure of the third gas, 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 of the gas,
R is the ideal gas constant (0.0821 L atm/(mol K)),
T is the temperature in Kelvin.
We rearrange the equation to solve for P:
P = (nRT) / V
Now we can calculate the partial pressure of the third gas:
P3 = (0.110 mol * 0.0821 L atm/(mol K) * (273.15 + 43 °C)) / 9.00 L
First, we need to convert the temperature to Kelvin by adding 273.15 to 43 °C (316.15 K). Then, we substitute the given values into the equation.
P3 = (0.110 * 0.0821 * 316.15) / 9.00
Calculating this expression, we get:
P3 ≈ 0.386 atm
Next, we calculate the total pressure by summing the individual pressures of each gas:
Total Pressure = Partial Pressure of gas A + Partial Pressure of gas B + Partial Pressure of gas C
= 0.257 atm + 0.579 atm + 0.386 atm
≈ 1.222 atm
Therefore, the total pressure after adding the third gas will be approximately 1.222 atm.