A vessel of 6.84 L in volume contains 3.61 L of pure water at 25°C. A partial pressure of 3.67 atm of CO2 is quickly injected into the space above the water. Calculate the partial pressure of carbon dioxide remaining once the solution has become saturated with the gas. Henry's constant for CO2 at this temperature is 0.0350 M atm-1
so the initial moles you get using PV=NRT, so N=PV/RT and same for moles final (diff volumes used of course) but I think that's where I'm messing up. Because after that you divide by a volume, then by the concentration. But I think I'm messing up what volumes go where. I know what the answer ius supposed to be and I cant get it for the life of me. I'm thinking that for inital moles the volume would be 6.84 cause that's the whole thing. And then I'm thinking for final moles it would be 3.61 cause that's where the liquid is. But I don't know what I would divde by...the leftover 3.23? anyways I've tried many combinations and I cant get it. ANy help would be greatly apprecaited. I could be totally on the wrong track. Thanks
To solve this problem, we can use Henry's law, which states that the concentration of a gas dissolved in a liquid is directly proportional to its partial pressure above the liquid. The equation for Henry's law is:
C = k * P
where C is the concentration of the gas, k is Henry's constant, and P is the partial pressure of the gas.
In this case, we want to find the partial pressure of CO2 remaining once the solution becomes saturated. To do this, we need to determine the concentration of CO2 in the solution.
First, let's find the initial moles of CO2 using the ideal gas law, PV = nRT:
n_initial = (P_initial * V_initial) / (R * T)
where P_initial is the initial partial pressure of CO2, V_initial is the initial volume of the vessel, R is the ideal gas constant, and T is the temperature in Kelvin.
Given:
P_initial = 3.67 atm
V_initial = 6.84 L
R = 0.0821 L*atm/(mol*K)
T = 25°C + 273.15 = 298.15 K
Substituting the given values in the equation:
n_initial = (3.67 atm * 6.84 L) / (0.0821 L*atm/(mol*K) * 298.15 K)
Now, we need to calculate the initial concentration of CO2. The concentration can be obtained by dividing the initial moles by the initial volume of the vessel:
C_initial = n_initial / V_initial
Next, we can use Henry's law to find the concentration of CO2 once the solution is saturated:
C_final = k * P_final
where C_final is the final concentration of CO2, k is Henry's constant, and P_final is the partial pressure of CO2 remaining.
Given:
k = 0.0350 M atm^-1
Now, we can substitute the values and solve for P_final:
C_final = C_initial = k * P_final
Rearranging the equation, we get:
P_final = C_initial / k
Substituting the values we calculated earlier, we have:
P_final = (n_initial / V_initial) / k
Now, let's calculate the final partial pressure of CO2:
P_final = (n_initial / V_initial) / k
= [(3.67 atm * 6.84 L) / (0.0821 L*atm/(mol*K) * 298.15 K)] / 0.0350 M atm^-1
Evaluating the expression will give you the partial pressure of CO2 remaining in the solution once it becomes saturated.