Heyy, okay I have this question about chemistry and its driving me nuts. It feels like I am so close but am just missing something. The question is:

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

Okay so I know basically this...we dicussed with some other people and rearrganed equations and basically got this:
(mol initial - mol final)/V = concentration x pressure.

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

I understand your frustration, but don't worry, I'm here to help you out! Let's break down the problem step by step to find the correct solution.

The first thing we need to do is determine the initial moles of CO2 in the vessel. 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, R is the ideal gas constant, and T is the temperature.

Given:
Initial volume (V): 6.84 L
Initial pressure (P): 3.67 atm
Temperature (T): 25°C (which needs to be converted to Kelvin by adding 273.15)

Using the ideal gas law, we can calculate the initial moles (n_initial) of CO2:
n_initial = PV / RT

Substituting the given values, we have:
n_initial = (3.67 atm) * (6.84 L) / (0.0821 L atm/(mol K) * (25 + 273.15) K)

Simplifying the equation, we get:
n_initial ≈ 0.883 moles

Now, we need to use Henry's law to find the final pressure of CO2 once the solution becomes saturated. Henry's law states that the amount of gas dissolved in a liquid is directly proportional to its partial pressure above the liquid. The equation is:
P_CO2 = k_H * C_CO2

Given:
Henry's constant (k_H) for CO2 at 25°C: 0.0350 M atm^-1

We need to find the concentration (C_CO2) of CO2 in the liquid phase. Since water is incompressible, the volume occupied by the liquid remains constant. Therefore, we can consider the final volume (V_final) for calculating the concentration.

Given:
Final volume (V_final): 3.61 L

The concentration of CO2 (C_CO2) is given by:
C_CO2 = n_final / V_final

Now, we need to find n_final, the final moles of CO2 in the vessel. We can use the equation you mentioned in your question:
(mol_initial - mol_final) / V = C_CO2 * P_CO2

Simplifying the equation:
mol_initial / V - mol_final / V = C_CO2 * P_CO2

Since we know the initial moles and the initial volume, we can rearrange the equation to solve for mol_final:
mol_final = mol_initial - C_CO2 * P_CO2 * V

Substituting the values we know:
mol_final = 0.883 moles - (0.0350 M atm^-1) * P_CO2 * 3.61 L

Now we can use the given information and rearrange the equation again to solve for P_CO2:
P_CO2 = (0.883 moles - mol_final) / (0.0350 M atm^-1 * 3.61 L)

Substituting the values we know, we have:
P_CO2 = (0.883 moles - mol_final) / 0.12635 L atm^-1

To find the partial pressure of CO2 remaining once the solution becomes saturated, we need to find mol_final and substitute the value back into the equation.

Let's assume the final moles (mol_final) is equal to the moles of CO2 dissolved in the water, which means no CO2 remains in the gas phase. Then substitute the value of mol_final into the equation, and calculate P_CO2.

Once you substitute the value back into the equation, you should be able to find the partial pressure of carbon dioxide remaining in the vessel. I hope this explanation helps you understand the steps required to solve the problem.