A 9.80-L container holds a mixture of two gases at 39 °C. The partial pressures of gas A and gas B, respectively, are 0.426 atm and 0.832 atm. If 0.250 mol a third gas is added with no change in volume or temperature, what will the total pressure become?
The easy way to do this is
p 3rd gas = nRT/V, then
pA + pB + p3rd = Ptotal.
You can do it the long way this way.
n gas A = PV/RT.
n gas B = PV/RT
n third gas = 0.250
ntotal = nA + nB + n3rd.
Then Ptotal = nRT/V
You should get the same answer either way. I believe the answer is close to 1.91 atm but check that. I may have punched in a wrong number.
To find the new total pressure after adding the third gas, we need to use Dalton's law of partial pressures. According to Dalton's law, the sum of the partial pressures of all gases in a mixture is equal to the total pressure.
First, let's calculate the initial total pressure before adding the third gas.
Initial total pressure = Partial pressure of gas A + Partial pressure of gas B
Initial total pressure = 0.426 atm + 0.832 atm
Now, let's calculate the moles of the third gas added. It is given that 0.250 mol of the third gas is added.
Now, the volume and temperature remain constant, so the gas laws can be ignored. Therefore, we can assume that the added third gas will not affect the partial pressures of gas A and gas B.
Thus, the partial pressures of gas A and gas B will remain the same after adding the third gas.
So, the new total pressure will be the sum of the initial partial pressures of gas A and gas B, plus any additional pressure contributed by the third gas.
New total pressure = Partial pressure of gas A + Partial pressure of gas B + Pressure contributed by third gas
Pressure contributed by third gas = (Number of moles of third gas / Total volume) * (Gas constant * Temperature)
Gas constant (R) = 0.0821 L atm mol^(-1) K^(-1) (universal gas constant)
Total volume = 9.80 L (given)
Temperature = 39 °C = 39 + 273.15 = 312.15 K (temperature in Kelvin)
Number of moles of the third gas = 0.250 mol (given)
Now substituting the values into the equation:
Pressure contributed by third gas = (0.250 mol / 9.80 L) * (0.0821 L atm mol^(-1) K^(-1) * 312.15 K)
By calculating the expression, we get the pressure contributed by the third gas.
Finally, we can calculate the new total pressure by adding the pressure contributed by the third gas to the initial total pressure.
New total pressure = Initial total pressure + Pressure contributed by third gas
Calculating this expression will give us the final answer, which is the new total pressure after adding the third gas.